The logic is sound, but the assumptions are faulty. Therefore the final conclusion is bad. It's like any process, if you input garbage you're not going to receive anything but garbage.
The particular faulty assumptions here are, I believe, 'sex/gender is solely related to genes/genitals' and 'sex/gender is binary'. The latter is just a particularly common faulty assumption, down to 'scientifically there are two genders' rubbish. But if you start from those two assumptions and try to use logic to get to a reason why people socially and physically transition you get to something along the lines of 'to gain access to women only spaces', and from there it's a short trip to 'transwomen are abusers'. Unfortunately I can't explain in more detail, as I don't know formal logic, but it's a pretty basic GIGO case.