It's actually the opposite, at least where I'm from (especially with 'educated' or 'professional' men). It's not uncommon to hear women complaining about the man shortage. First random google link and link a more different random google link both seem to agree.
I know at times it certainly seems the opposite (a few girls I know are rarely more than a few days without some poor bastard hanging off their every word) but, that said, it's reasonably uncommon for any of the guys I know to actually pursue girls. When they do it seems they have a high strike rate of girls that are interested in staying with them. That's even true with me, which is a bit odd to think about as I've just gone through a massive stint of being single...But within a week of me showing even remote interest, way more of the girls I know were seriously hitting on me than I would have expected.
I know at times it certainly seems the opposite (a few girls I know are rarely more than a few days without some poor bastard hanging off their every word) but, that said, it's reasonably uncommon for any of the guys I know to actually pursue girls. When they do it seems they have a high strike rate of girls that are interested in staying with them. That's even true with me, which is a bit odd to think about as I've just gone through a massive stint of being single...But within a week of me showing even remote interest, way more of the girls I know were seriously hitting on me than I would have expected.