Fascinating, if somewhat confusing at times, discussion. I'm sure there are some trans people for whom the root cause of their feeling trans, or at least part of it, is to do with entrenched beliefs about gender differences at home and / or elsewhere. However, I'm sure there are lots of other causes and in most cases it probably won't just be one thing (it's all a rich tapestry). The problem for me is that currently trans is presented as the cause, the issue, the thing, and the answer. Once a person realises they are trans, that is often seen as explaining everything. Sadly for a long time no one has been allowed to talk about trans as if there might be any underlying cause, or multiple causes, instead we have had to accept it as both the cause and the symptom and even trying to ask why it is that some people end up feeling this way was seen as close to genocide. I am quite sure that trauma is involved for many, but that doesn't automatically mean 'blame the parents' in all cases. Many parents try very hard in difficult circumstances but things happen outwith our control, or we do and say things without fully understanding the implications, or we are angry or tired or sad or stressed and we let our kids down one too many times as a result. I'm sure in many cases, it is a result of a fetish and I'm afraid I've never been brave enough to delve more deeply into how or why they develop. I'm sure societal expectations and peer pressure play their part. In the old days people worried that anorexia was caused by pro-ana websites, skinny models and so on. The anorexic girls I knew either had a lot going on at home or, looking back, were probably also autistic, and lived in a world where skinny was worshipped. So it was part of it but probably not the full story.
My heart goes out to any parent going through this; almost all parents only want whats best for our kids and do the best we can with the sense we have.