I recently posted my opinion about this halacha but I can’t find it to link you the whole discussion, but maybe someone else knows where it is.
Basically I do not think this has anything to do with a man being inherently better than a woman. We have no right to judge who is better or worse. But it is a halacha about survival. The halacha sees men as more capable of cultivating our social norms/culture/religion etc., and therefore it’s more important to save the man. It is like if in the middle of the war you can save either the general or the philosopher, you save the general, not because he deserves to be saved, but because he is a better protector of the society as a whole, and thus in this context he can be described as more important. But in truth that isn’t necessarily accurate.
This is the link you refer to: