It is unfair for those people who want to pursue other dreams that are not mentioned in the film. The Republic categorized the citizens as Philopher kings (gold sash), warriors (silver sash) and artisans/producers (bronze sash). They have to take a certain exam to determine where they fall, and for those who failed will not be given the chance to prove themselves worthy. Unfair isn't it? Well what's more is that parents were not to have eternal bonds with their child. They are, i think, to be separated upon birth.
Although, the idea of doing just one job is a good thing for there is no unemployment, there would also mean that there would be no change, right? which is not good for it means that the citizens are not improving at all. There would be no change in one's activity everyday which would make life living there a big BORE. What if a person wants to be someone else, like a warrior wants to become a philopher king? Would he be punished?