For example: If a person tells another person, "You're racist" and the other person responds, "No, I'm not racist. But I just don't like to see Black and White people dating because it's not right", then the other person responds back, "Thanks for making my point."
How about self-defeating? From Lexico:
self-defeating: (of an action) preventing rather than achieving a desired result; futile.
The person in your example is making a self-defeating argument, thereby inadvertently making your point for you.