When something that sounds easy (eg accepting a trans person’s chosen gender identity because “it doesn’t hurt me to accept someone’s identity”) turns out to be, well, not so easy, I wonder why… what is it that people feel threatened by?
The patriarchy is based on the superiority of the male/masculine over the female/feminine; so a male who doesn’t present as masculine is disparaged as being effeminate or even as emasculated.
Praising “strong independent women” actually reinforces the patriarchy by still positioning those masculine ideals as being superior, and just accepting that some females can achieve them as an exception - but at a price (that is why successful women are asked how they balance their family commitments with work, but men are never asked that. Also while we have awards for female entrepreneurs we don’t have awards for house-husbands)
If people were allowed to freely choose their gender, it would make this vector of discrimination impossible - someone who was supposed to be the subaltern (by virtue of sex characteristics at birth) could just become male and gain membership in the dominant class. This would be like a peasant becoming a noble or a low-caste becoming high-caste. Trans sexuality must be denied for the patriarchy to continue.
The weird thing is that while it is mostly the masculine identity that is threatened, and that too by female → male transitions, the the biggest target of transphobia is male → female transitions, in the guise of “protecting” women (but maybe not so weird, because only the dominant group can protect the subordinate group - so the mere notion of “protecting women” reinforces the patriarchy)