Trans women point clearly to the fact that gender exists only by cultural definition, not the reverse.

No one denies that gender is cultural. The argument is whether gender is (i) a cultural adaptation to differing innate drives that correlate highly with anatomical sex (with due regard for all sorts of outliers) or (ii) a political move by men to oppress women. Radical feminists believe the latter, but the very possibility of being trans points to the former. So, radical feminists deny that one can be trans in any direction. It's not about narrowing the definition of "woman" but simply denying the possibility of anyone being trans, full stop.