Completely wrong. Just because a man's and a woman's brain don't look any different to the naked eye, doesn't mean that there aren't differences at the microscopic level. Decades of research on a variety of different animal species show that there are significant sex-specific differences between male and female brains, which drive many aspects of adult social and sexual behaviour (and also responses to injected hormones). Microscopic examination of transgender people's brains after death have shown that certain sexually dimorphic regions are a lot more similar to cis people's brains from the gender they identified as, rather than their birth sex. Other things that suggest there are important differences include experiences of people such as myself (who are biologically male but were prenatally exposed to synthetic female hormones, and who've had female brain development take place as a result), and people like David Reimer (who was born male but raised as female, unsuccessfully as it turned out, after his penis was destroyed during a botched circumcision).
