Makes you realise how little critical thinking many have. Only women have periods isn't saying every woman does. Just that if you do then you are a biological woman and not biologically male. Swathes of 'I'm menopausal am I am man" logical leaps 
If anyone can identify as a woman the term becomes meaningless. Is that really what anyone wants? How does this help identify and redress inequality to women?
And this is essentially what's been said. The backlash is truly baffling and depressing.