Right. That's the definition the international Olympic committee tried to enforce. The presence of a Y chromosome meant athletes weren't allowed to compete.

The problem is that many women (who are not trans) have a Y chromosome. They are either XXY (Klinefelter), or XY (Swyer), XY mosaicism, or any of the other intersex conditions.

Are those people not women? They may have fallopian tubes, a vagina, and a uterus, but also a Y chromosome.