Actually, from his perspective I think John appears to feel the same way. Since Karkat is going backwards through the timeline, he is basically going through the friendship in reverse. From his side, they've both slowly fallen in hate with each other.
I think the experience is pretty similar to them both. Using John's subjective timeline as a reference, at the beginning John was annoyed, while Karkat was almost friendly, and said that they would inevitably become friends. And then John learned more, and Karkat hadn't learned as much yet, and in the end, Karkat hates John and John acts friendly, and says that it is inevitable that they will become friends. And then the friendship kind of rubs off on Karkat like some infectious meme, pouring more water into the self-fulfilling time mill.
And anyway, Karkat is most likely (?) incapable of combining genetic material with John. Different species, different universe, different concepts romance. Do they even have the Matriorb anymore, or did they need to use it to make themselves or something? I don't think they're going to be able to consummate their hatred in the foreseeable future, which is what I meant when I said their relationship was doomed.
Also, I just realized that Karkat saw John bleed and knows he has red blood. LOOKS LIKE ANOTHER THEORY DOWN THE DRAIN!