Addressing a common “Gender Critical” argument
This isn’t just a tongue twister, this is a serious and surprisingly not that rare “Gender Critical” (GC) argument against the assertion that trans women are women. The argument goes: if you are asserting that trans women are a type of women, then you must also be making the assertion that women are all trans women. The implication then being that this second assertion is trivially false, therefore the first assertion must be false too. Yes, you read that correctly.
This is a very fundamental misunderstanding of logic, specifically set theory. It can be quite easy to understand why this argument is so ridiculous by using the same argument in a different situation:
If lions are cats, then are cats lions?
No. All lions are cats, but not all cats are lions, for example tigers. This means that lions are a subset of cats, which is the mathematical term for “is a type of”. Lions are a type of cats, trans women are a type of women. You can represent a subset with a Venn Diagram as shown below.
This argument against trans women being women thus does not hold up. The second part of it “then you must be asserting that all women are trans women” is false — that assertion is not implied.