No, you miss my point. If gender is social, but the current social idea of gender is that it is not social, it’s not true, is it? The social construct is a false one. Like believing in the Aether, or magic, or that sun is pulled by a chariot of the gods, or that women have one more rib than men, or that malaria is caused by bad odours. Those are all social constructs but we know they are also false. Believing gender is an innate “identity” in the soul, is a false social construct, since gender is actually a set of social scripts to “conform” to and not an ineffable presence.
What you are arguing is that gender is performative (this comes from Butler’s use of Austin’s performatives - parts of speech that only work as forms of social performance). Butler used this to argue that gender was essentially (that is, completely or only) performativity - it only exists inasmuch as it is performed socially as a construct and there is no underlying non-social essence.
That is completely at odds with the idea that gender is an inner psychological phenomenon, part of a soul, biologically innate in some people’s minds so that “trans brain scans” can reveal it, or in some other way a non-social phenomenon. You cannot have social construct and not a social construct at the same time. “Construct” literally means built out of (from construere). If what you meant is “bits of it are social and bits of it aren’t” then that’s a different thing; but that then isn’t a “social construct”.
Butler herself has completely gone back on her original argument now because gender activists don’t like the idea of gender as performativity, but somehow that doesn’t seem to matter…because ineffable, mystified incoherence is the order of the day in gender theology.
Hurrah for the new gender mystics! There is no logic but a set of self-appointed gurus for the gender-religiose to argue about on the internet. You say one thing, try to pin down a term or two; but that is never what they really meant at all….