* Why is this trope misogynist toward women? Men get described for it just as often (I think) for it.
** Because when men sleep with multiple women, they are considered by their peers (mostly male ones, but sometimes quite a few women as well) to be awesome. When women sleep with multiple men, they are considered by their peers (most of their male and female friends) to be "slutty". That said, some women will call out a guy on this (sometimes he is called a "manwhore") but it is still more rare, and many men and women will still praise them. Also, some women will just say they are "empowering themselves" when "overly sexualized"...but they are still looked down upon by the majority.
*** You shouldn't generalize quite so hard; as a male, I can say with confidence there are plenty of guys out there considered "manwhores" by their fellow men. Contrary to common belief, a lot of the time, guys are not praised for sleeping around. However, the perception that it's okay for guys to sleep around is definitely prevalent in the media.
** But the page quote is a male example! Come on!
*** Yeah, but no one's saying that the trope as a whole hasn't been applied to examples from both genders; just that there's a DoubleStandard whereby a man has traditionally been celebrated for sleeping around where a woman conversely has been vilified. It's the DoubleStandard that becomes misogynistic, not the trope as a whole. The page quote is hardly particularly unflattering to the male example it discusses, after all.
** It's not so much the trope itself, which is pretty equal-opportunity, as the way it's normally used. If the work itself doesn't have a DoubleStandard, the audience reaction will.
** Additionally, it can be said that, since AManIsAlwaysEager, men are low-hanging fruits on the casual sex scene so luring into bed isn't that difficult for a woman. Women, on the other hand, should abide by the MyGirlIsNotASlut rule, meaning that respectable women are frigid and prude. Thus, getting one into bed is like hunting a much more elusive quarry.