Comparisons to discussing religion with someone who has very different beliefs comes to my mind when I watch that video. I've had a similar conversation in the past, after reading through the Bible and then trying to talk about it with a very rigid Christian, though he was alone so it wasn't quite so asymmetric. But when something, whether secular or not, is a question of faith, people get very upset and defensive or they try to convert you with a small set of approved tenets.
When the conversion doesn't happen anger might follow or perhaps a pseudo-pious wish that the other person might one day see the light (receive Christ, have a trans person in the family etc.).
I think the foundational tenet in the gender identity belief system is that mantra I have seen so often in social media (trans women are women, trans men are men, nonbinary are nonbinary). Anyone who doesn't accept it is a heathen or a heretic, because that's what the whole edifice depends on.
But it also means that nobody can be 'woman' without having that unverifiable/unfalsifiable/ inner feminine feeling, and that nobody can be a 'woman' based on the sex of her body.
So their belief system violates my identity (embodied, based on living in a female body and how people with those bodies are treated), forces me to pretend to have a feminine 'soul', threatens my rights, and makes fighting sexism almost impossible.
I wish transgender rights didn't get pushed within that belief system, because it is not possible for me to accept it. It's not transgender people but those who created this edifice that I find truly troubling and hostile.