I hated Carver so much, up until the point he became a grey warden or betrayed the templars to side with me. He was so whiny and just UGH...reminds of my actual little brother*before he matured*...so yeah.
Carver becomes a better character if you take into consideration that he's desperately trying to find some purpose in life? His grouse nature towards the other party members seems in keeping with this, because while he desires a sense of comraderie and kinship with the people he's fighting alongside, he's very much aware that these are Hawke's friends and not his.
His wanting to be part of something is why he jumped at the chance to fight in Ostagar, become a mercenary or smuggler, tried to join the Kirkwall guard, went off to join the Templars or despite not intending to join, ultimately found a place with the Wardens?
His comments in Legacy if he's a Templar, that he always secretly wanted to become a Warden, makes me think that he'd probably be one of the Templars who deserted the order to join the Wardens, as mentioned in "Last Flight".
(Incidentally, my own headcanon for why a Rogue/Warrior Hawke was at Ostagar is because Carver had stupidly signed up and when they found out they couldn't drag him back home without him being hung for desertion, they signed up as well to keep him safe.)
So yeah, Carver's a jerk... but I can get where he's coming from... even if that doesn't stop me wanting to punch him at times?