> "Let’s not put pressure on people only because we want them to adhere to what we believe is right and normal."

You're 100% right, and yet... this is not really cultural, it's mostly innate and evolutionary (even among animals it's usually the male who initiates).

Even if society stopped putting pressure on this "who's gonna initiate" nonsense, women will mostly prefer to "wait" and men will be obliged to initiate (otherwise, no dating and no relationship).