Those are the finer details of why New Atheism turned into an engine of transphobic bigotry.
If you want a simpler explanation though, it's this: toxic masculinity walks hand in had with gender conformity and transness violates the assumptions of gender conformity.
The rest is just intellectual rationalization of a prejudice they felt in their guts toward us because we threaten a sense of cis male entitlement bound in the comfort of sex/gender conformity.