I'm a guy in my 20s and have heard this excuse for why men are the ones who overwhelmingly approach. But I think it's ******** to be honest.
Talking to most of my male friends, they don't have an issue with women approaching them. The only guys I know are extremely traditional (usually older generation 50+).
What I think is going on here however is that most of the women that approach guys are not really attractive. Think about it. Women get way more sexual attention (flirting, catcalling, being asked out etc) than men. Women who are average to hot will get this a lot, especially in their 20s. In this case, why would they need to approach
Women who are below average to ugly however will seldom/never approach. So they have to take the initiative and ask guys out. Most guys don't find them attractive so it gives off the perception to other women that guys don't like being approached when in reality, they just don't like being approached by unattractive women...Good looking women are another story.