I always wonder why people think that there are many parents who want their children to be transgender when they aren't.
The assertion seems to be something along the lines of Munchausen by Proxy, which is essentially when a parent fakes an illness for their child in order to get attention for themselves. While this is a real mental illness and form of child abuse, I do believe this argument is rooted in the belief that transgenderism (especially among children and teens) isn't real. You don't really see the same accusations being directed towards the parents of most sick children despite it being more common to use illness than to use transgenderism (I am not personally aware of any confirmed cases of Munchausen by Proxy through transgenderism)...
Note: I am not claiming that transgenderism is an illness.
For this particular instance, I think this had to do with people believing the parent that is vocal. Luna's mother decided she wanted to keep things private while the father has been out running the christian and conservative news rounds. I understand the mother's choice to try to keep her child from becoming a national point of debate, but having only one side of the story made it so easy for those who wanted to see this as a crazy liberal mother forcing her child to be trans. It takes someone going through court records to find the other side of things and you see that what we heard was only the father and his friends while we missed the testimony of Luna, two therapists, a CPS agent, Luna's twin brother, and the mother herself.
All that said, I again cannot blame the mother. Near the end of the video in the OP the author talks about how Luna's mom had a twitter account where she would post helpful little tips for parents on all kinds of topics like making sure kids where sun screen in the heat and he would read it from time to time. Before the author posted the video, Luna's mom actually killed this twitter because every post was getting incessantly hammered for the Luna issue by conservatives. The video author talks about how this affected him and he wasn't sure why because seeing the actual abuse hadn't really had such an effect. He came to realize that he had been ascribing this almost saint-like resilience and perfection on the mother, that as long as she could ignore all the hate this was just an internet argument that hadn't affected her life. Seeing her kill the twitter was a reminder that she isn't impervious to this, and while we all debate about these things on forums there are real people on the other side of these issues often times getting hurt.
To be fair, I'm somewhat hamstringing the discussion to talk about that portion of the video, but I found it poignant and wanted to hear others' thoughts.