Why? If anything, I thought the TERF sort hated transwomen, especially the ones pushing the "cotton ceiling" concept.
TERFs, which is to say a subset of Radical Feminists, believe that all gender concepts are learned environmentally. Therefore they believe that all transpeople absorbed the idea that they have the wrong body to match their personalities. And that the idea that certain personalities/lifestyles are "masculine" or "feminine" is false categorization (which is pretty true), and that such categories contribute to men learning to be more violent and women to being more subservient. So therefore, transition not only will not "work" for an individual, whose problem is views as unhealthy conditioning, but it also supports sexist views of gendered social structure. Basically.
Other Radfems who are not anti-trans believe in the neurological concept of sex dysphoria, and/or that choosing to live your life how you want isn't necessarily "gendered", but that you should keep in mind how it affects others.
So-called TERFs hate transwomen in particular because they believe that TW mostly are perverts (a common opinion of TW) and also that males, being raised as men, are raised to be violent. Many groups also disapprove of the use of "lesbian" and believe it should be used exclusively for females attracted to females...but we all know penises are female now, so, that argument goes off topic pretty fast.
Anyway, lesbians and transmen have had a strained relationship for decades, since (until recently?) the majority of transmen lived as butch lesbians prior to transition. So there was a lot of personal feelings involved besides the political ones, especially since the Second Wave, wherein many lesbians chose to reinterpret their relationships as also being a political act. (So it was sort of like tumblr way before tumblr.)
Worth noting that (a) not all radfems/lesbians feel any of these ways, and (b) women who date transmen sometimes identify as "straight" and sometimes as "lesbian", so terms are really up in the air.
If you want to see anti-transmen drama, look at Dirtywhiteboi, who is arguably fighting transtrending, but does so in the most sociopathic way possible. (A really scummy person, really.)
