Because otherwise some people's fragile sense of self will break.
That's the bottom line isn't it?
And they want to be treated as if they are women. But we are pretending they really ARE women so it can't be AS IF they are women.
When actually most women just want to be treated like a human. With the same courtesies and respect and rights as the other half of the population. There are a few situations where, due to biology, women need special provisions - space/facilities/dignity in dealing with menstruation, breastfeeding, childbirth.
Transwomen don't need that, will not have spent teen years anticipating or learning to deal with that. And unless they are really out of touch with reality can never expect to. And therefore is it any surprise that women may feel uncomfortable with transwomen around when dealing with the specifics of biology - menstruation/breastfeeding/childbirth/menopause.
Now if the transwomen is very low key and not directly involved in care - in the "just want to pee and leave" camp, then a lot of women don't make a fuss.
But lots still care.
Why is that so hard?