SOME POSSIBLE SPOILERS IF YOU HAVEN'T WATCHED AOU OR THE CW TRAILER.
I'd go with bits and pieces of both Norrelken and Omegacron's answers.
I don't think it's that Steve likes war. I think it's that being a soldier is all he has left.
The thought of going home is a nightmare because he literally has no home now.
He lost his first chance at going home when he went into the ice. He started to take a few tentative steps to re-establishing a home in TWS after Peggy tells him essentially to 'start over' and Sam asks him what makes him happy. His response? He's thinking of what he could do if he wasn't in S.H.I.E.L.D. and even makes an attempt to ask out that cute nurse.
Except five minutes after he does, Nick Fury's bleeding out on his floor, he finds out the cute nurse was a S.H.I.E.L.D. agent in disguise, and a mere 24 hours later, everything in his life is upended again. Steve insisting that S.H.I.E.L.D. be dismantled in TWS is in some ways just as life-shattering as going down with that plane -- it was the one foundation he had up until that time.
So at the end of TWS, Steve's lost his chances at a home not once, but twice, his best friend has been brainwashed, and Peggy's losing her memory. He's becoming more and more rootless.
In Ultron, we find he's been trying to find Bucky without success, has apparently tried to get a place where he used to live, but it's wildly different and out of his price reach (btw, an apartment in Red Hook can go for two million now, at least -- and this was a place that used to be tenements in Steve's day!) and even the fight to end HYDRA which had given him some sense of purpose seems to be ending.
And then of course, we see the Witch's nightmare. To me, his nightmare means:
Steve wants to go home. Steve wants to be more than a soldier. We see that both with his nightmare and with his reaction to seeing Hawkeye's home -- and that moment itself is masterful both in his small sigh, where he's positioned in the doorway (on the outside looking in) and then how he turns, walking away, so what we see is the shield, not the man, walking away from those dreams.
And notice, Steve's the only one who really breaks out of his dream, too.
It's also why he reacts so violently when Tony braces him about going home. He's tried. He literally can't. He can't go back in time, his attempts at creating a new place have fallen through, and there is literally nothing for him but being a soldier.
By the way, that's not blood in that scene, it's wine. That scene is particularly well done to portray how someone with PTSD would perceive that situation. The noise is too shrill, too loud, the flashbulb pop startles him and makes him flinch, as does the popping champagne cork, the first thing that comes to mind when an obviously sauced guy spills red wine on his shirt is blood, and what he notices is not the dancers, but two guys about to duke it out.
We've seen from his opening scene in the Avengers that he's got the classic PTSD flashbacks (and probably nightmares; he certainly does in the comics.)
Steve's nightmare, as shown to him by the Witch, is wanting to go home, wanting to be more than a soldier, but never being able to do so. He's buried himself in being a soldier because it's all he has left, but he literally doesn't know what he'll do without that purpose. That's supported by the deleted scene in AoU in which he's talking to Hill, and claims that if Ultron brought piece, he'd hang up his shield. Hill gives him a 'yeah, right' look and says, 'Would you?' And for a split second, there's a look of fear on Steve's face as that hits home. He doesn't want people to suffer. He doesn't want war -- but he literally has no other identity, no other place where he belongs anymore, and nothing left but that shield.
I don't think we see a truly content Steve Rogers at the end of AoU; even Tony (who is about as perceptive as a brick) notices he's not really okay. But he's accepted that Steve Rogers' dreams are not achievable and being Cap, being a soldier, is going to be the closest he can ever have.
Which, of course, is why Ross's ultimatum in Civil War is going to hit him where it hurts. Do what he believes to be right or give up his one semblance of home and the one thing which gives him a sense of purpose?
He's Cap. We know what he chooses. But it'll still hit him hard.