Byrne's argument requires essentialism about womanhood to generate determinate membership conditions, but essentialism about gender is philosophically untenable given intersectionality.

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Byrne(as the author of the argument being critiqued): A philosopher whose argument is being evaluated in this statement; without more context, this likely refers to David Byrne or another contemporary philosopher who has written about what categories like 'woman' actually refer to.
Determinate membership conditions(in relation to defining who counts as a woman): Clear, specific rules that tell you exactly who belongs to a group and who doesn't. Like how 'being over 18' are determinate membership conditions for voting—there's no ambiguity.
Essentialism (about womanhood/gender)(as applied to gender and identity): The idea that being a woman means having some core, unchangeable feature or set of features that all women share—like a biological trait or fundamental nature. It's the opposite of thinking womanhood is socially constructed or variable.
Philosophically untenable(The verdict on Heytesbury's conflation)

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