“No one would ever transition just to get a scholarship, win a race, or otherwise gain some unfair advantage over women.”
This objection is responding to a strawman – few, if any, critics of transgender theory believe that men regularly transition exclusively as part of a cynical ploy to access resources or activities normally reserved for women. It seems reasonable to assume that the majority of transgender people sincerely believe the claims they make about their gender and sex, and see access to sex-specific accommodations and activities as a logical consequence of those beliefs rather than the motivation behind them.
However, just because someone sincerely believes they’re entitled to something doesn’t mean their entitlement can’t be irrational, problematic, or harmful. In fact, some of the most destructive behavior in our culture arises precisely because people are acting out of a deep-seated conviction generated by their foundational assumptions about the world – no one considers it particularly comforting to hear that, for example, religious fanatics who want to ban abortion are doing it because they really, truly believe that life begins at conception. Transgender activists who point out that no one would ever transition purely for personal gain are similarly missing the point. A male person’s earnest belief in their right to violate common-sense sex segregation policies and appropriate women’s resources is merely evidence of oblivious entitlement, which is hardly better than naked self-interest. What ultimately matters is the harm these actions bring to women; the internal motivations of those who choose to harm them are ultimately irrelevant.