Note: If you have not read Kakashi Gaiden in the Manga, (It hasn't been animated) then this will contain spoilers. Read at your own risk. (Kakashi Gaiden is Manga Chapters 239-244. Part Two of the Naruto series begins at chapter 245)
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This is just a list of reasons why I think the couple makes sense and should have been. And hey, if a miracle happens, Obito might end up alive again, and I can say it SHOULD BE. x3
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If you don't want to read every little detail I wrote, there's a cute little list at the end of the detailed list with the same reasons, only without the details x3 And people told me I couldn't really rant about Kakashi and Obito as a couple for five hours!

(Honestly, though, this is so much faster to read than to write... I know because I re-read it to edit it XD)
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So let's start with chapter one.

Obito and Kakashi don't exactly have a "Love at first sight" relationship. They argue, appear to dislike each other, and Kakashi is always criticizing Obito. Kakashi is always complaining about how Obito is always late, he insults the Uchiha Clan because of Obito, and Obito later has nothing to give Kakashi for his first day as a Jounin, and Kakashi doesn't mind (Since the gift would be coming from Obito).
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Chapter two:

Kakashi gets injured, and Obito yells at him for saying his wound was "fine". Kakashi told Obito he didn't want to talk to him, saying, "I don't want to talk to you. The "Elite Uchiha", a coward and a crybaby!"
Once again, they were starting to get into an argument. When Minato (Fourth Hokage/Yondaime/Obito and Kakashi's sensei) starts telling Kakashi that rules and regulations are important, but not everything, and that he must adapt with the situation at hand, Obito points at him and says, "Hah! Look!" Seeing this, it seems both Kakashi and Obito will jump at the other with every chance they get.

Later that night, Obito speaks with his sensei, and brings up Kakashi. He admits he knows Kakashi is an amazing person, and before saying this, he calls himself a loser.
"Ah... No. Thought I'm called "Elite" because I was born into the Uchiha clan, I'm a loser. I acknowledge that Kakashi's an amazing person, but..."
Minato also tells Obito the story of what happened to Kakashi's father, and Obito appears sad about it. Minato also tells him, "Obito... Understand him... Even a little... Don't bear a grudge towards him."
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Chapter three:

Having heard the story of Kakashi's father from Minato the night before, Obito appears to want to try getting a better relationship with Kakashi, by calling him "Commander", instead of complaining about the fact that Kakashi was going to be leading their team while Minato was away. He doesn't exactly appear to WANT to call him this, but he makes sure to let it out. Kakashi and Rin are surprised by what Obito said, and Minato is happy for him.

Later, Obito and Kakashi fought an Iwagakure Shinobi together, and it was Obito who started working with Kakashi, a sign that Obito may have wanted to start getting along better with Kakashi.

When Rin is kidnapped, Kakashi and Obito get into an argument about saving her. Kakashi insists he and Obito continue on together with the mission, but Obito insists they go to save Rin together. Both of them try to get their points through, but it seems neither of them are willing to listen to the other, and they only seem to want the other to agree with THEIR point. When Kakashi says being a tool to complete a mission is the most important thing, and that emotions are unnecessary things, Obito asks him if he seriously thinks like that. Kakashi pauses a minute, looking saddened by what Obito had just asked, remembering his father. Hiding his sorrow, he tells Obito, "...Yes... That's right..."

Obito finally gives up on Kakashi and starts to walk away. Kakashi tells him he doesn't understand anything, then says, "What happens to those who don't follow the rules...", but is cut off by Obito, who says "I believe that the 'White Fang' is a true hero..." Kakashi is surprised, and Obito continues. He says, "Of course, those in the Ninja world who break the rules and regulations are called trash... but... (The next panel shows an apparently sad Kakashi) those who don't care about their companions are even worse trash." Kakashi stills seems saddened as Obito keeps going, saying, "Anyway, if I'm that kind of trash, I'll break the rules! If that's not being a true Shinobi... then I'll crush that idea of a Shinobi!" He walks away with the last part.
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Chapter four:

As Obito walks away, Kakashi doesn't seem to have been fazed by anything his teammate said, and his expressions returns to it's normal, calm expression. He, too, walks away, and the two part ways.

When Kakashi is next shown, his injured arm throbs, and he stops moving, remembering that Rin told him yesterday that his wound was pretty much healed, (After she'd healed it) but if he overdid it, the wound would re-open. He remembers this sadly, then sadly remembers what Obito had said to him just recently. He also remembers when Minato had told him that rules and regulations were important, but they weren't everything. Once again, after remembering what Minato told him, he remembers more of what Obito said to him. (Most of what he thought about during that scene were the things Obito said to him) At that point, he apparently chose to turn back and follow Obito.

When Obito is next shown, he is about to attempt to save Rin, but an Iwagakure Shinobi, (The one that knocked Rin out and kidnapped her) appears behind him, and attempts to attack him. He is saved by Kakashi, and he says, "Ka... Kakashi... You... ...Why?" Kakashi brushes it off by saying he can't leave it up to a crybaby Ninja like Obito, while Obito can't think of anything but the one thought: '...Kakashi...'

When the attacking Iwagakure Shinobi mistakes Kakashi for his father, Kakashi tells the Iwagakure Shinobi that the sword he's using is a memento from his father, which tells us that he really DOES have emotion, and that he just HIDES it. (In other words, he has hid his emotion this entire time, up until Obito spoke with him one-on-one, with nobody else there to stop their argument. He's just now showing his emotion)

Obito remembers what Kakashi said-- that being a tool was the most important thing, and that emotions were unnecessary things. Again, he has no other thoughts, besides, 'Kakashi... You...'

The Iwagakure Shinobi says, "...I see... The 'White Fang's brat... There's no need to worry in that case..." He then uses his Iwagakure special jutsu, and blends with his surroundings, concealing him. Kakashi realizes that they can only track him by movements in air currents and sound. He tells this to Obito, who asks Kakashi, "Wh... Where is he?" Kakashi quickly notices by sound that the enemy is behind and about to attack Obito, and shouts, "Obito! Behind you!" Obito was too slow to react, and Kakashi rushed over to save and protect him. In the process, however, Kakashi's left eye was slashed, making him lose his vision in that eye. Once Kakashi fell to the ground, Obito ran over to him, tears in his eyes, screaming for his teammate, then asking Kakashi if he was okay. Kakashi doesn't respond to his question, but tells him that the enemy is skilled, as their enemy had already disposed of the kunai with Kakashi's blood on it. By this point, Obito is already crying. Kakashi asked him if he had dirt in his eye again, and told him Shinobi don't cry, that he wasn't dead yet. Obito paused and remember what Minato told him after he'd spoken to Kakashi the day before. After telling Kakashi to adapt to the situation at hand, he'd told Obito he was wearing goggles, he couldn't have gotten something in his eye, and if he didn't learn to control his mouth, that not only would his mouth, but his mind would also become weak.
Obito realizes he's always mouthing off, that everyone is always saving him. His next thoughts were, 'I'm just a mouthing-off loser... ...But...'
Kakashi reminds Obito not to let his guard down, and Obito remembers what he told Kakashi in their last argument. When the enemy attacks again, Obito strikes him down, this time protecting Kakashi. He reveals his Sharingan, which he had just newly activated. As the enemy falls to the ground, Obito says he will protect his companions.
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Chapter five:

Kakashi pauses a moment in hurt. Obito asks him if he's okay. Kakashi tells Obito that it seems his left eye is completely useless. He says he'll fix himself up with Rin's  medical pack, the one she gave him the day before, which was his first day as a Jounin. He then says, "Let's go rescue Rin right away!", showing that he's chosen to help Obito in the end.

When they begin fighting their next enemy, their show of teamwork is incredibly good for them never having gotten along before.

Later, after they rescue Rin, the enemy uses a jutsu that creates a landslide. When Kakashi is hit with a falling rock on his new blind spot, he falls to the ground. It was Obito that immediately ran back to save Kakashi. When Kakashi sees Obito crushed by the boulders that otherwise would've crushed him, he immediately tries to lift the boulder to save his teammate. Obito tells him it's enough, and that it looks like it's over for him. He says it right side is completely crushed, that there's no feeling in it.
Kakashi wonders what kind of commander, what kind of Jounin he is, and Obito remembers that he never gave Kakashi a gift for becoming a Jounin. He tells Kakashi he'll give him his Sharingan. He then says to Kakashi, "The villagers... No matter what they say... you're an excellent Jounin... That's how I feel... Please take it..." (Translation differs from two internet translations I have seen, as well as the translation from volume 27, but it's all based on the same topic, so none of the translations are too far apart in words) Obito also says he'll become Kakashi's eye, and that they'll see the future together.

Kakashi is seen crying on the last page of the chapter.
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Chapter six:

Kakashi fights for Obito, and when more enemies come and use the same jutsu as before, Obito tells Kakashi and Rin to leave, and gets crushed by the other boulders. His last thoughts are directed towards Kakashi, and was glad to have finally become friends with him. Kakashi's thought of the moment was only, 'Obito!'

Kakashi soon tells Rin he would protect her with his life for Obito. (He says Obito loved her, she was important to him, and that because of that, he'd protect her with his life. This is implying he's only helping her for Obito) He admits to Rin he was once the kind of trash that would abandon her. This tells us that Kakashi was completely changed by Obito.

Later, Minato tells Kakashi, who had just woken up, (He'd apparently fallen unconscious during the fight, when Minato had arrived) about how he managed to make it to where he and Rin were, since Kakashi asked. He then tells Kakashi he was sorry he couldn't make it in time, that Rin told him everything.
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Smaller/Shortened hints:

Obito and Kakashi did not have a good relationship to start with. It wasn't anything like, "Love at first sight".

Obito admits to Minato that he knows Kakashi is an amazing person.

Obito calls Kakashi "Commander", instead of complaining about Kakashi leading their team.

Kakashi is saddened when Obito is talking to him at a point during their argument. He had never shown any signs of sadness before this point.

Out of the things he remembered when his injured arm began hurting again, four of six memories were of Obito.

Kakashi went back to help Obito, Obito having changed him.

Kakashi and Obito had an excellent show of teamwork, considering before then, they'd never gotten along well at all.

Before Obito died, he left Kakashi with kind words.

Obito's last thoughts were of and directed to Kakashi.

Obito gave his life to protect Kakashi-- not Rin. Kakashi was the one who would've otherwise been killed, if Obito had not been, and thus, he gave his life for and saving Kakashi.

Although Obito is said to like Rin, this is never shown as anything more than friendship love. He just wanted to save his companion. Throughout the story, no hints were given that he liked her; we only just found out in the last chapter, in which Kakashi only said he loved her, that she was important to him. As that IS true, he also loved KAKASHI, and KAKASHI was ALSO important to him.

The main plot of the story revolves around Kakashi and Obito.

On a side note, Kakashi and Obito are seen, most of the time, next to each other, or one behind the other in a line. There were only two times I know of off the top of my head that Kakashi and Obito were not next to each other, which was after they'd just argued in the first chapter. Obito was behind Minato while they were walking, and was next to Rin when Kakashi was about to attack the Iwagakure Shinobi, Mahiru, with his Chidori, that he was still working on.

Now that Kakashi is years older, to be the man as we know him now, he has taken on several of Obito's traits, one of them clearly being that he is always late. He spends his time at the grave that has Obito's name it, which always makes him lose track of time and end up late to wherever. Kakashi also says what Obito said to him-- that people who didn't care about their companions were even worse than trash.
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This may not seem all that much, but within the borders of only six chapters, I'd say it's a TON.

Yes, I know guys don't usually fall in love. But if I cared, I would not have bothered to write this, now would I have? But it's not impossible, guys falling in love. (What is the Anime/Manga Loveless? Chopped liver? O_o)

So yeah... I'm finally out of things to say... ^^;