You may think that having high self-esteem is always a good thing. It's the fuel that makes you get out of bed and ready to kick some ass. In the 80's, America was swept by the self-esteem movement - the idea that, if kids had high self-esteem, they could face life's challenges and rise to any occasion. You might have heard of stories where teachers were forbidden from marking papers with crosses, to avoid the risk of damaging a child's self-esteem. What actually happened, some argue, was the production of a generation of self-entitled brats with massive, unfounded egos - who couldn't handle the merest hint of criticism. There's a great article about it (and Jersey Shore) here.
In the world of Psychology, some researchers are arguing that the downsides of having high self-esteem is a great deal of narcissism and lack of empathy for others. Our generation get accused of thinking we're special and wonderful all the time, but it's clearer to see in others. We probably all know someone who poses for countless selfies, who obsesses over their clothes and make-up, and who seem to only talk about themselves. Despite having high "self-esteem", those people are often the most sensitive when it comes to criticism, too - their ego may be big, but it's fragile.