(((tpnd))) i used to feel the same way. i'm so sorry you feel that you have to prove something to them. the good news is you don't .
what i learned in therapy was what i was looking for was validation of myself from them. in my case it was mainly family that never seemed to validate my feelings or who i was and had become. with the help of my T i discovered that maybe those i cared about the most would never give me the validation i sought. there was comfort tho in knowing who i had become. so as long as i knew who i was, their opinions didn't really matter. it was difficult at first to use this tool, to not feel hurt by their actions. sometimes i just had to mentally remind myself that i knew who and what i was. i would ignore any mixed messages from them like, "well, you know how ____ is." and it would be sarcastic. as time went on using the tool my T gave me it really didn't matter!!! i was very comfortable with who i had become. as long as i knew who i was, that was the important thing.
i hope this reply will help you in some way. i like you for who you are right now!!