For me, the problem with including a definition of female as "having a gender identity that is the opposite of male”, is that it should include a similar definition of male as "having a gender identity that is the opposite of female” - oyherwise you're excluding trans-men. And that creates a ahort of a linguistic loophole,a catch-22 if you want, or a tautology, as female would then be defined as "having a gender identity that is female".
To your first point, have you checked out the definition of "male" in Merriam-Webster? To your second point, I don't think there's any tautology. The dictionary is saying that one way "female" can be defined is according to how a person self identifies. This is distinct from other possible definitions, such as the ability to bear young or produce eggs.
For me, the problem with including a definition of female as "having a gender identity that is the opposite of male”, is that it should include a similar definition of male as "having a gender identity that is the opposite of female” - oyherwise you're excluding trans-men. And that creates a ahort of a linguistic loophole,a catch-22 if you want, or a tautology, as female would then be defined as "having a gender identity that is female".
To your first point, have you checked out the definition of "male" in Merriam-Webster? To your second point, I don't think there's any tautology. The dictionary is saying that one way "female" can be defined is according to how a person self identifies. This is distinct from other possible definitions, such as the ability to bear young or produce eggs.