You'd think, but no.
The only technique I think has a chance of working with these sorts is to give them a few facts that counter their narrative and the narrative they see all the time - yes, people under 18 are getting hormones and surgery, no, puberty blockers are not harmless and reversible, no, it's not just 'people doing what they want with their own bodies', they're actively forcing it on everyone. I can never remember the exact years, but there's the statistic from the UK that for, like, the last ten years there were literally zero trans murders, but more than one murder committed by someone trans.
But you give them those few facts, only a few, and then you let it go. Because as
@sheepworldvizor's link points out, they're not going to be persuaded by facts. So drop a couple that specifically counter whatever bullshit point they're holding on to - they're all bullshit points and they've all got counters - and then let it simmer. After that, it depends on the person - but don't be the one bringing up the topic, don't berate them, just know your shit so you can correct them if they start in, but you have to let them do the mental work of connecting the dots themselves.
One of my friends is a social worker who's quietly quite TERFy but still believes the crazies are the loud but extreme minority of TRAs. Letting the stories of crazy troons build up, especially when they are so-called 'leaders' of the movement, helps there, because I can point to anything from TransLifeLine to the guy working for WPATH running a fetish site for underage castration to all the troons, from Lucas to Alex Carabello to Rhys 'Veronica Ivy' McKinnon, who have threads here and are treated as spokespeople (I'd use spokesmen, but Chase Strangio counts) for troons in general. Not directly to the Farms, sadly, but definitely to all the articles that are linked here, and the tweets by these deranged assholes shooting their cause in the foot.
Just knowing it's a male Scottish social worker, I'd be tempted to just point out exactly what JK Rowling said in her statement that murdered millions of troons, her history of being in an abusive relationship, and then all the hatred, death and rape threats she gets on an hourly basis. It's also a good litmus test because what she said boiled down to 'biological sex is real', and if he disagrees with that then yes, he's a lost cause. But you know him better, so the only real advice is to be polite, firm, and
sparing. All you can really do is try and get him to start noticing, because no one sane who starts to doubt the troon narrative has ever become
more convinced by their cult.