I think the really interesting bit (that I don't think TRAs are at all conscious they are doing) is sliding the meaning of 'women' within the same thought, or even sentence.
To even be able to observe the original group pattern - Group A report higher levels of X than Group B (a simple example being, "women report higher levels of neuroticism than men") you have to have had at least one qualifying criterion for membership of Group A and Group B in the first place, and that criterion cannot be X (because X is the thing you are measuring - it was, at the start of your investigation, your unknown about which you were hoping to get an answer).
In reality, the original criteria for Group A is (and what TRAs know, on one level of their doublethink, that it is), has to mean 'adult+human+female', otherwise they're is no place to start. So what is being said originally is:
Group A [=adult human females] report higher levels of X [=neuroticism] than Group B [=adult human males].
If after getting that result you then try to mentally redefine Group A as, "anyone reporting higher levels of X", and Group B as "anyone reporting lower levels of neuroticism", you are now simply saying:
Group A [=people who report higher levels of neuroticism] report higher levels of X [=neuroticism] than Group B [=people who report lower levels of neuroticism].
Which is technically true, but tautologous and tells us nothing.
OR, a variation: if after getting that result you then try to redefine Group A as, "adult human females PLUS the portion of Group B reporting higher levels of X", and Group B as "adult human males EXCEPT those who report higher levels of X", you are now saying:
Group A [adult human females PLUS the portion of Group B reporting higher levels of X] report higher levels of X [=neuroticism] than Group B [=adult human males EXCEPT those who report higher levels of X].
Which is a partial tautology, artificially inflating the result you were investigating and ends up telling you little to nothing.
However, people rarely slow their thinking down and set it out clearly step by painstaking step in order to spot the fallacy, particularly when they are motivated NOT to try to spot it.
It's fascinating (and depressing).
To bring this back round to Atwood: perhaps unfairly I've always had the impression that she's a bit "I'm not like the other girls" and I think this comes through in interesting ways in her writing (even The Handmaid's Tale). Part if that, I think, is that she considers herself to be far more logical and 'no nonsense' than most. For that reason I'd be really interested to hear her taken through some of the rationale by someone like Helen Joyce, who is similarly data-driven, logical and straightforward but lacks whatever motivated reasoning seems to be operating on Atwood. Unfortunately I expect Atwood would not she to that as it's easier to handwave it all away than risk engaging and being confronted with uncomfortable fact and logic.