This really is such a maddening mantra:
"Women do not need to prove they are women."
They never had to when they were excluded from society across numerous areas, so that justifies giving a man a certificate which no one can ask for/see, that capitulates women's boundaries for his demands.
Men can't prove they're women so this helps justify bypassing any requirement to explain the 6ft2 bloke in the female changing room/hospital ward/prison wing/sport, wide a side of 'only bigots question' for kicks.