Be honest about why you want to win. Proving something to someone is heavy fuel.

Motivation built on proving somebody wrong burns hot and runs out, because it depends on an audience that may not be watching. It also lets the doubter choose your direction, so you can end up chasing something you never wanted. Anger will carry you through the first few months. It rarely carries you through the boring years in the middle.

Ask what you would still want to be good at if the person you are proving something to vanished tomorrow. That answer is the part worth building on. Use the anger if you have it, and keep checking it is not the only fuel you are running.