I'm married. I have only my own dozens of years of anecdotal experience of myself and others. Your world view of "exactly the same" can't be changed, but simple testosterone and estrogen differences alone would argue a lot of differences for the average person.

When women start asking men out at a similar rate as men, then maybe there isnt a "natural relationship" anymore. A large preponderance of data from places like Tinder, OK Cupid, etc completely contradict you in a very statistically signifiant way. Call it cultural all you want. I'm just going to call it common sense.