I'm curious to know why you're bringing the concept of "patriarchy" into this discussion? Do you think Musk's gender has anything to do with his actions and behavior?
This is effectively a Elon indulging in the worst forms of toxic masculinity. Meanwhile he’s also humiliating himself. I don’t think he yet realizes that people aren’t going to forget this. Every interaction he has with someone he’s going to feel naked due to how much of his hand he’s let people read.
Whether he does it consciously or not, if your model of musk is a Macho whose "honor" has been impinged (by himself, but also public snipes at e.g. his private jet while posing as the man to save the climate with Tesla) and who's pettily trying to pettily re-assert his "manliness" then you've been getting a lot of ROI out of the predictions that has allowed you so far.
Toxic masculinity is manifested through pathological subduing of emotions, mindless stubbornness, excessive pride, inappropriate violence, misogyny, and homophobia.
If you want to apply the concept of toxic masculinity to someone it would be more appropriate for Bezos or Andrew Tate. Musk isn't behaving like that at all, and I don't like your casual misapplication of it because I can see that it's simply politically easy, misandrist, and above all, wrong.