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Carlos Zambrano gets booed for three reasons:
- he celebrates every strike out like he won the World Series
- he can be very inconsistent; he's a Cy Young candidate one game and the next looks like one of the worst pitchers in the league
- his temper; he's gotten into several fights with teammates
Baseball fans expect a little bit of class from the players and when they celebrate an out in the fourth inning like you would the final out of Game 7 of the World Series, they take issue with it (Zambrano isn't the only one that does this). This is why Big Z gets booed everywhere on the road.
Baseball fans also expect their own players to be very good, all the time. Cubs fans will boo Zambrano because he (like A.J. Burnett or Daisuke Matsusaka), has a problem with consistency. All players have bad stretches during a season, but when you come out and say "I'm going to win the Cy Young", you need to pitch like it game after game. This is why Cubs fan boo him.
Baseball fans want their players to have some fire. But, if that fire is constantly getting you ejected or fighting with teammates, they're not going to like it. This is another reason Cubs fan boo him.