I've just been reading this (not sure how to make a clicky link, can someone do it for me? ) www.bailii.org/ew/cases/EWHC/Fam/2016/2430.html
It's findings from a court case about custody for a 4 year old boy, whose mother insisted he was a girl despite no evidence that he behaved any differently from other boys.
The paragraph below, which is talking about the boy's mother, seems, to me, to explain why the TRAs just don't engage in debate, and present illogical arguments - the confusion this generates causes immense cognitive dissonance and leads to other people believing in the Emperor's new clothes.
'... illogicalities characterise M's evidence. Nobody has doubted that M is both articulate and intelligent and so the reasonable inference is that she must recognise some of the illogicality of her own statements. I consider that she has learnt that by creating 'confusion', to use Ms Sambrooks' word, amongst the professionals, she generates a situation in which her own distorted beliefs gain greater traction and are able to prevail with less effective challenge.'
I think I finally get where the TRAs are coming from!