It doesn't say "a person producing, at conception, the small reproductive cell." It says "belonging, at conception, to the sex that produces the small productive cell." AKA XX and XY. You belonged, at conception, to the sex that produces the small productive cell, Matt. I know this is a shock, but you did. The fact that the organs take time to develop doesn't change that your biological sex is determined at conception. Is the spermy an x, or a y? That's the heart of the issue.
Imagine Biology 101 being so far beyond the intellectual scope of so-called keyboard warriors. Ugh.