Finding out how few transwomen had medical transitions.
My first real experience was seeeing someone in a cabaret group that I like who is a transwoman - wears women's clothes/style/name, but deep voice, so fits nicely in the group. And I just always thought of her as 'she', despite knowing that - old-school style trans I guess.
And occasionally reading a bit more about people like that, difficult back stories, having to come-out, bullying, difficult childhoods, etc, make me feel sympathetic, and that these were people who were victims and needed sympathy. And in some ways I do still feel that.
Equally, for quite a long time, having a relatively sheltered and non-diverse upbringing, not knowing that many women who couldn't (for religious reasons, for example) be in a place with men that they were expecting to be single sex. Not knowing personally people who'd experienced domestic violence, or serious sexual assault etc. So I wasn't all that aware of how many women these things affected, and as a result, I thought that being kind to a small number of people who had very difficult backgrounds would be OK. This was hugely strengthened by a feeling of guilt(?) about how people who were homosexual had been treated for years, misunderstood, not accepted etc, and an eagerness not to want to do that again to another marginalised group.
Finding out more about women who were victims was part of changing my mind. Finding out how many transwomen didn't have surgery, or who did it for reasons other than gender dysphoria also helped. Realising that many of them did not have the sort of troubled backgrounds that I had imagined added to it. Then all the stuff about sports, changing rooms, awards, short-lists, etc and realising that women were losing out - it made me realise that being sympathetic was also harming women, just not in perhaps such an obvious way. It is sometimes easier to feel sympathy for a specific transperson who is there in front of you (or, well, in the media) with a difficult and sympathetic back story, than it is to think about a more hypothetical, nameless group of women who didn't get into the race/didn't go to the changing room/don't go to the public loos etc.