I'm going to ignore the bonkers brain scan post, but for me Artichoke's statement gets to the nub of this:
The whole world does not revolve around male people, their wants, their needs, their feelings and their rights. Female people have rights too. Including to have access to toilets.
There's a key difference between 'wants' and 'needs'.
It's never really been defined by those championing trans rights exactly the nuance between these, probably because the starting point is 'Transwomen are Women' so we're coming at this from very different places.
From what I've seen, a massive % of the trans rights campaign seems to be based on 'what I want' rather than 'what I need'.
But I'm going to take a stab based on reading lots around this from lots of perspectives on the difference between 'wants' and 'needs'.
Males who identify as women :
Need : some of these males who identify as women (not all, see people such as Fionne and Miranda} need spaces away from other males who don't identify as women, as some of those males may reject and potentially be violent to them.
Want : some of those males want to use female spaces for a variety of reasons. a) believe they're truly women b) want the validation of others accepting/tolerating/giving in to their demands that they're women, c) other reasons that must not be named on Mumsnet!
Females
Need : based on evidence, design of space by other campaigning females (and organisations, eg, see many NGOs campaigning for single-sex spaces in refugee camps etc) single-sex facilities for the reasons of privacy, dignity, and also safety.
Want : Some females would like space away from males. Others are fine with sharing all their spaces with males, whether that's in the supposedly benign toilets, to the very real women who are tonight in prison forced to share their shower area or even their cell with males. Right now, in social-media-world, and at organisational and system level, the 'want' from females who are up for sharing all spaces with males who say they're women seem to be overwriting those females who don't want this.
There's a difference between wants and needs - and, as I read somewhere else today, creating policy and law around 'wants' rather than 'needs' is not a good direction of travel.
For the OP, what your colleague 'needs' and what your colleague 'wants' may be two very different things.