Part of the reason Price got booed for struggling is that he is just not all that LIKEABLE at this point. Part of that is his fault, part of that is not his fault at all.
One of the reasons he's not very likeable is that he has just waltzed in and been handed the keys to the kingdom without ever having had to earn it. This happened in Hamilton, where he walked in and played the playoffs on a very good team that was going to win anyways, after the team had great goaltending all season long. The other guys got shit on, so Price looks like a bit of a villain there. Not his fault...that was all Canadiens management making that call. Then he comes into Montreal and is given the starter's job in short order without ever having outplayed Huet. Again, not his fault, that was all management. But when they threw him in there and he went into the playoffs without a safety net and shit the bed, it caused many a grumble and generated more ill-will.
As for factors that are his fault, there's his off-ice drinking and excessive partying that has clearly affected his game at times. There's the way he ballooned into a fat pig last year. I know a lot of people are irritated by how laid back he is when playing...he doesn't BATTLE enough...he doesn't push guys in front of him or peek around guys to try to find the puck when he's being screened. It seems like he just gives up on plays too easily, unlike the Marty Brodeurs and Patrick Roys of the world who fought tooth and nail every minute of every game. That certainly isn't winning him many fans.
I know I reached my breaking point with Price the day after he hit his Patrick Roy pose. When he sat down at that press conference and did his little "I hit the pose on purpose to remind the fans that booing doesn't help". In a situation where he should have shown some remorse he threw out a 'be careful what you wish for' vibe, and that's where I decided I had a strong dislike for him. My attitude was "Fuck you, you snot-nosed little punk...who do you think you are? When Patrick Roy did it, he already had 2 Stanley Cup rings, 3 Vezina trophies, and had been the best goalie in the league for the better part of a decade."
Carey Price was already under a microscope because of decisions management made, but the stunt he pulled in the last game and the subsequent arrogance he showed at the end-of-season press conference are his own doing. He's going to have to live with the concequences now; for his sake, I hope he's stellar right out of the gate next season.