They have a right to build the mosque and I have no problem with it being built. Like most emotional topics, groups of people feel betrayed when the government uses logic and reason to make a decision rather then illogical emotion. That is the government's job though.
A parent doesn't buy a kid a candy bar when they kick and scream and say they hate them because the parent said they wouldn't. There is logic behind the parents reason and only emotion behind the kids.