Again, this is scientific absolutism, which is fine, but besides the point. Yes you're right. You can't look at an individual's skin colour, hair, etc and with 100% accuracy determine their ancestral heirtage. Especially if you want to be really accurate about where in Africa or Europe say, they came from. Granted.

The central point here, the entire reason we're having this discussion, is how you leap from this, to the idea that it's valid for people to claim whichever race they choose to as their own.

Why are you not okay with determining race by physical characteristics, but fine with determining it by an individual's gut feeling? Please actually answer this question.