Why do I have to prove myself to others?

You don't have to prove yourself to others! You really only ever have to prove yourself to you. You are the most important person in your life, and you only have to take care of yourself, at the end of the day there is no opinion that should matter in your life other than your own. Society always puts pressure on us to prove ourselves to others, but you just have to avoid giving into those pressures in favor of taking care of yourself, and doing what makes you the happiest. tl;dr, you don't have to prove yourself to anyone.

Actually, we don't need to. Everyone has different perceptions and what is success to one may not be a success to another. In my opinion, instead of proving or competing with others, we should focus on our personal growth and live this short life in a way we find worthy. I have read in an article that most aged people regret that they haven't lived their life in the way they wanted. Giving away our joy for chasing the dreams that are glorified by the people will not give us satisfaction. So I tell myself live life the way I want and try to strive and prove myself more than others. Hope this helps