Another girl coming to weigh in.
One of the reasons I have to mention is the society. We live in a society where it is acceptable for a guy to spend an entire day gaming simply because video games are stereotypically more associated with guys. During my teenage years, I had to press the window button and hide my game every time my mom entered my room, because she would literally (not exaggerating) scream at me to stop playing just because I'm a girl. Also, if mentioned in a conversation, "she plays video games" sounds degrading when referring to a girl. So, the society itself discourages women from even attempting to play video games, let alone actually pursue any serious gaming plans.
Next, of course, there is an undeniable sexism. Before playing League of Legends, I played World of Warcraft, which is a much more sociable game due to actually being able to sit around and chat. It also had PvP ranks, and no matter how high I got on the PvP ladder, I was never taken seriously, and I would always be put aside for some other guy when making PvP teams. I don't know if it's some kind of a "bro code", or something, but I was more likely to be mocked than, god forbid, admired for my skills. The same goes for this game. If I were to actually climb to the challenger, I have no doubt in my mind that any team would more likely choose another guy player who is perhaps slightly worse than me. Plus, if by some chance I were to be chosen, everybody would automatically assume that it was because of my gender and not because I deserved it. So, either way you look at it, my effort would never be appreciated.
Another sexism is the more direct one. Personally, I didn't get many "go to the kitchen" insults here, perhaps because people are less likely to assume that I'm a girl (who even pays attention to names in a 30-60 min games) but in WoW, I got plenty of those. The beauty of the Internet lies in its anonymity, and with it comes the comfort of not having to show anybody respect. So, if a guy gets offended by anything at all, and he knows that I'm a girl, I know that I'll be sent to the kitchen, metaphorically raped, or worse. It's simply not a healthy environment for any girl, especially not a young one. So, again, discouraged from an early age to even try.
Taking all of that into consideration, knowing how much time it takes to actually master this game, and knowing how low the chances are of actually being chosen to become a part of a professional team, it's really not hard to see why a girl would not be bothered to play this game professionally, or any other game for that matter. It's too high of a risk, not high enough reward, no respect from the society but more likely to be shamed, and it requires seriously thick skin to handle the male-dominated gaming world on the Internet.
P.S. I main Rakan, and I also like Thresh, Nocturne, Brand, Jhin, Skarner, Zilean, etc, so the argument that girls only play female champs does not hold water. I mean, people tend to look for a way to connect with what they play, so yes, my favorites are Vayne, Lux, and Leona, but I would not go out of my way to pick a female champ.