TERFS are anti-trans for the polar opposite reason as SoCons. SoCons think it's wrong or anyone to deviate from the gender matching their sex, while TERFS think gender is completely made up so there's no such thing as really being trans. That really is the logical outcome of all feminist thought which most of them refuse to acknowledge resulting in their having incoherent positions on things. If there's such a thing as being trangender then there is obviously such a thing as gender in the first place and it is not just a social construct.
Not all feminists deny gender, though obviously that seems to be the radical feminist position.
For what is worth, I haven't seen many TERFs taking that position. The more common argument I've seen is that being a woman is biological in nature and therefore any trans woman is really a "man in a wig" no matter what they do.
Another argument I've seen is that the existance of trans women "devalues" femininity in some way.
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