First, I have to express a general objection to “you have it easier than I have it” arguments. On those rare occasions when they’re not cringe-worthy examples of self-pity, they’re still churlish and pointless.
Next, I’d have to point out that women do a lot of the asking nowadays. And if you think asking a woman out takes nerve, try asking a man out. Frequently, they’re so stunned or offended (yes; apparently being put in a traditionally female gender role makes some guys feel so “gay” that even the realization that “hey, this woman finds me attractive” can’t redeem their fragile heterosexual ego identification) that they respond quite rudely. They don’t have that lifelong schooling women get on how to say no in a nice way.
When a man asks out a woman, his worst fear is that she’ll turn out to be a gold-digger or fatter than she looked at first. A woman’s worst fear in accepting a date is that he’ll turn out to be a rapist or serial killer.
And even back when it was unthinkable for women to do the asking, women did not have it easier in dating. First of all, not every woman gets asked. That’s where terms like “spinster” and “old maid” came from – punishing terms for women who “failed” to attract men who would take care of them. And what if you find yourself getting asked out only by married men and creeps? Why, you had a choice: suffer the stigma of being an “old maid” or make do with whatever cretins were available to you. How lovely! How easy! All you had to do was feel shame until your self-worth fell into shambles ’round your feet, and subject yourself to Harry, the guy who hangs around the school playground a little bit too much. (And don’t forget: if you have kids with Harry and Harry molests them, we’re blaming you!)
I could go on and talk about how rare it is that men actually make the first move (guys, we’re taught from very early on how to rope you in subtly so you think you made the first move). I could list the time, energy and money women who get asked out a lot often invest in cosmetics, clothing, accessories, learning coy body language and those subtle techniques I just talked about, and learning to appeal to the male ego before “just sitting around waiting to get asked”. But it’s been done. And of course, you can just open your eyes.