The simplest metaphor to describe Karkat is that he is the gay kid in high school constantly screaming homophobic slurs in the desperate hope that no one will catch on, and that he might even be mistaken. Most of the abuse Karkat directs at others is really just camoflauging the abuse he wants to direct at himself! Because he really, really hates himself. He bitches and rages about past him and future him, but he really does know that all these versions of him are him. And as a result, he constantly bitches at them, because he knows they're going to make the wrong decisions- Because he honestly thinks he himself is going to/have made the wrong decisions.
He honestly hates everything because of that thirteen years/six sweeps of self-loathing. Karkat is easily the most human of the trolls, and if you tell a human kid that if he slips up at all he'll be killed for something he could never help, it's going to feed into a lot of issues. Karkat doesn't hate anyone half so much as he hates himself. Which is not to say he does not hate others! He really, really does. But at least a lot of it is redirecting his own issues elsewhere.
That's why he's constantly spewing abuse at everyone, really. Even the people he really likes! He has no idea how to act any other way. He's like a puppy that's been abused all its life, and now he can't help but growl and bite whenever he sees a person, no matter what that person is doing, or what he thinks of them. He just can't figure out how he can be nice to people. Even when he's trying to be nice (like with Jade!) he can't do it without heaping on abuse at something.
His drive for a kismesis and matesprit and all four quadrants is... well, partially he's a dorky kid. That just can't be helped. But aside from all that, he really just wants to be accepted for who he is- and what he is is a mutant freak with no powers and nothing going for him in a society where darwinism and casual murder reign supreme. He screams as loud as he can all the time, because he just wants someone to acknowledge him. Even for a kismesis- Hell, even Jack, who was constantly stabbing him and such. Karkat didn't care- It was attention of a sort, and Karkat, so desperate for acknowledgement, siezed upon it.
Which leads to the humans. Karkat was starting to get over himself and even grow attached to the humans! He's realized that they are really just dumb kids like him, and now that they're no longer some simple omnipotent force with no rhyme or reason but cheating him and his friends- friends, real ones (more on that later)- out of their just reward. He was starting to accept them for the dumb kids they are!
... and then AU week happened. Karkat has the memories of being human, and of being on his human equivalent's planet, and what he saw terrifies him, perhaps more than Gamzee ever did.
He was happy as a human.
He was still a mutant, but he was the only one who cared, and he definitely wouldn't be killed for it. He had to lead everyone, and even if he annoyed them, there was no worry of the group descending into a pile of murdering each other. He led the team, he did his best, and it was working out. As a human, he had managed to reach the God Tier, which was, as Hussie stated on his old formspring, a full realization of who he is.
At first, he just tried to repress this. He couldn't deal with it! He tried his damn hardest to just forget AU week ever happened. He was doing okay, even, though being a lot grumpier.
And then he canon-updated.
He knows, back in the veil, he fucked up beyond belief with Terezi. And this hurts him, because out of everyone, Terezi doesn't just accept him and his freaky blood, she actually likes him better this way. And that means more than he can ever say. And that's a big reason he hates Dave so much. Because that candy-red that Terezi likes so much? Dave has it too. And Dave's not some dorky kid with a mountain of issues and self-hate. Dave is the coolkid. Not just a coolkid, but the coolkid.
And even more importantly, everything is falling apart around him. Kanaya, who he really cared about, killed by Eridan, who he really did consider a friend, if a kind of pathetic one. Feferi, who he wanted to help Eridan with, and... was vaguely friends with! Also killed. Tavros, who didn't deserve any of this, also killed, at Vriska's hands. And Gamzee! His mOtHeRfUcKiN bEsT fRiEnD eVeR, turning around and actually, finally buying into the blood caste system, and deciding he wants to murder everyone. Because he can, and that's what he does.
And he can't accept that it just happened. It has to be someone's fault. And right now, that blame is falling on the humans, and then somewhat on Vriska. In fact, a lot of it on Vriska! But he can't manage to hate Vriska entirely- Okay, yes he can. But he can't fault Vriska for it nearly as much as he wants to, because... As far as Karkat knows, Vriska is exactly what a troll should be. Powerful, ridiculous, blue-blooded, killing anyone you please. That is how trolls are supposed to be, and this is exactly what Karkat is not. Despite himself, he wishes he could be like that! And then he hates himself a little more, for both not being like that, and for wanting to be like that. (Except for the romance, he fully looks down on her for that.)
Yet despite all of it, at the end of his session, he considered every one of the trolls a friend. He may not treat them with any form of respect whatsoever, but they were all friends. Or he thought so, anyway. And that was all he really wanted- A group of friends, who may not see eye-to-eye, but they look out for each other, and they don't try to kill each other.
Friendship means a lot to Karkat! It is a HORRIBLE DISEASE but he has gotten used to it. And now he doesn't want to go back to not having friends! This... seems to not be working out so well for him.
But all these friends, or what he thought were friends, suddenly all turning around and murdering each other has to be someone's fault. And while he's screaming and blaming the humans, and Vriska, and Eridan, and so on, really, he's covering up for the fact that he believes, not even all that deep down, that it was his own fault.
So for now, he'll scream, and rage, and blame the humans. And if it's the humans faults that everything has gone wrong, then Kanaya, his really good friend, deserves someone better than a human. And that's not even all, he's also in massive denial over ever having blackrom feelings for John. No one must ever know! So he... like I said, the gay kid screaming homophobic slurs. If he screams his contempt of humans the loudest, no one will ever think that he wanted to get his hate on with one!
Speaking of John and friends, at this point, he really does think of John as a friend. He can't ever bring himself to say it, but he doesn't even hate John anymore, and would rather be friends with him. And yet, he'll still spew abuse constantly.
That's just how he learned to be. He pushes everyone away, because he always had to. If anyone got close to him on Alternia, he could have been culled. So, even though he lived in the suburbs, he only ever cared about talking to the friends he only ever knew online. And even then, he would push them away, as he was terrified of what would happen if they found out about him.
I'm losing coherency here, so I'll just sum up: Karkat really, really just needs hugs. Lots of hugs.