Uh huh, then what race am I?

Is race passed down the mother's line? The father's? Or does it arbitrarily transform between generations due to some biological facts I'm unaware of?

Scientifically speaking, what are the rules?

I don't understand why you think your question should have a simple answer. 'Race' is, very obviously, a coarse division of human genetic diversity into a few clusters. That doesn't imply everyone fits neatly into one of the clusters. Saying someone belongs to race X is just a way of saying they are more similar to that genetic cluster/area than any other. Or to some point between two clusters, e.g. they are race (X + Y)/2 (Amerindian-Caucasian, for example).

Try applying the same logic to any other concept - it is nearly always the case that concepts in language do not perfectly describe the underlying reality. Yet we're not stupid enough to then claim that means the underlying reality is meaningless.

So it's a social construct...