Follow yourself. For whatever reason, your father is not able to provide you with the emotional support you need and should have without "proving" anything to him. I do know what this is like, I am no longer young but I grew up in a non-supportive household, being told I would not amount to anything, etc.
Anything you can do to increase your independence is good for you. Use the time away from home to make friends, get involved in things and build a supportive network. If you can work and manage school too, that would be good for you. You don't have to stop talking to your dad, but (this is hard) you could try keeping the conversations on the casual side, don't try to convince him of anything, you will continue to be disappointed. Unfortunately, he can only make changes if he decides to do that. Reason does not work in these relationships, it is all about emotions. Best of luck to you in your studies! Remember that he does say he is proud to others, he may be, he may also be jealous at some level. Clearly, he is insecure himself. But you can't fix that.
Live your life. Over time, it will pay off and it is possible the relationship will change, but not soon so exert your energies on building your self esteem and the world that You are going to live in.