Why is it that people are averse towards being stereotyped, or stereotypes in general (although they probably commit it themselves)?
This is because the very act of labeling or defining something is a political act. The moment you have defined something, you have constrained it into something you want it to be. This is an expression of power over the object you have just defined.
Powerful people the world over have exerted their influence by labeling, defining and stereotyping groups of people they wish to subjugate, because this sets boundaries on who they are and what they can do. This is the kind of soft power that works more effectively than pure force itself, because the moment a label you have been given takes root and gains acceptance, the more legitimate your limited place in relation to others will be. Your label takes a life of its own and does the job of keeping you in check for the labeler.
This is also the reason why it is so liberating to be able to resist being labeled. You could either be comfortable as what you're defined to be, adopting it as an identity, or you can prove people's stereotypes wrong, surprising them and smashing their stereotypes of you to pieces.