I agree that teaching logic would be useful but not in the face of a determination to adhere to otherwise nonsensical ideas because it is politically expedient. The references to Wittgenstein reminded me of the pickle Rupert Read got himself into a few years ago.
He wrote this very interesting article after the original Suzanne Moore / Julie Burchill hoo-haa:
blog.talkingphilosophy.com/?p=6662#comment-1120793
where he took a Wittgensteinian approach to the issue, particularly:
"It can't be that the feeling of feeling like a woman is in and of itself a complete, self-validating, "private" experience, of an individual (to see why not, Wittgenstein's anti-private-language considerations are helpful); the experience must have some content."
This went largely unnoticed until he was standing as a Green candidate a year or so later and was rounded on by Green TRAs. After an initial piece of self-defence (it's not transphobic to say X) he completely capitulated and prostrated himself before TRAs with this rubbish:
www.independent.co.uk/voices/comment/i-apologised-for-offending-transgender-people-but-that-wasnt-enough-10023116.html?origin=internalSearch
Of course, he doesn't make an alternative analysis where his original piece was wrong and comes up with a robust reason in line with his Wittgenseinian philosophy. He just says he has to choose his words to be more careful and caring.
This is in line with what you're saying Glinner that this is a corruption in our ability to think and to analyse critically. I agree that we have a responsibility to counter this in society. As Voltaire said, "those who can make you believe absurdities can make you commit atrocities".