"Women only play support" - or, why don't I play carry in Dota 2?

Hands up if you've ever come across the stereotype that women typically play support. No, not - I'm not armed, I'm just trying to - ok, show of hands, that's probably a better way to put it. I can't actually see your hands, but I know that it's a pervasive stereotype across all manner of gaming genres - MMOs, FPSs, MOBAs, etc.
It's not just a stereotype. I was recently in a Dota 2 stack with a bunch of female friends and we faced a hitherto unheard-of problem - we didn't have enough carry players. This is a pretty weird situation to be in - usually the carry is the most coveted role - but there we were, awkwardly staring at an empty safe lane as the timer ticked down.
Our mid player, Emmy, tried to whip us into shape using the powerful motivational tool, guilt. "Why do none of you play carry!?" she yelled at us. I looked down at my little lopsided skill triangle in shame. I've played over 2,000 games of Dota 2, and 1,970 of them were as support. You can gas me up all you like, Emmy, but if you put me in that safe lane I'm going to miss so many last hits (Dota thing, don't worry about it) everyone will report me, and my game will spontaneously uninstall itself and then eject my DVD drive and hit me in the shin.
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