The secret is in the latter half of the statement:
When you compare trans women to “actual women” you are being transphobic.
That’s what they’re saying is transphobic. Setting up a hierarchy of authenticity.
Saying that you are different from me does not mean I have a fear of you or that I don’t like you.
This wasn’t about you. Stop making it about you. This was about Liv, who compared trans women to cis men, called us rapists and invaders, and who very clearly fears our presence in women’s spaces.
It seems it would be more effective to let cis women know that trans women are different, but that doesn’t mean they’re any less human, and they deserve the same respect as everyone else.
That is exactly the opposite of what Liv is arguing, though, so you should probably take that up with her.