I feel like the root of most discrimination against trans people is a distrust or toxic idea about men.
For trans women, it’s the idea that they’re “men in dresses” or “men pretending to be women”, etc. etc. Even if that were true, what’s wrong with it? There’s nothing! It’s the idea that men are all sex predators that drives this – that if someone is “actually a man” then that means they’re inherently gross and dangerous to children and women.
For trans men, it’s just the same toxic masculinity standards applied to cis men. That they’re “too emotional” or “too weak” or so many other things that make them “not a real man”.
While this is certainly where certain flavors of transphobia originate, it’s important to recognize that a large portion of the hate directed towards transfemme individuals comes as a critique of feminine gender expressions which are ridiculed in comparison to masculine interests and gender expression. This is what they are referring to when they say transmisogyny.