I lovingly follow Playing D&D With Porn Stars (don't worry about that adult warning, it's very much like mine, "just in case") and I Hit It With My Axe. Recently Zak posed a certain question which raised my eyebrows and maybe something else. So I mulled it over while I searched for more similar photos, for research, of course.
One of my theories include, either these girls were hanging out with a certain type of guy. Proto-geeks, I guess I would call them. I was friends with a few and they could hide their nerd well when called for. they were on the varsity football team, they got horrible grades, one even went on a family hunting vacation every year and missed a month of school in order to kill things. BUT! they were my best friends through jr. high and early high school. they loved video games, had a good internet understanding and we played D&D, religiously. I've met a few guys who I think they turned into after high school/college and they're not particularly charming, nor do they outwardly display their nerdery as it would single them out as week and un-manly. I have also encountered the smokin hot chicks they attract and associate with, who . . big surprise, could, would and SHOULD be openly fantastically geeky. They are attracted to "jerks" which, oooh boy, we were, and then when confronted with a female either they hid the fact that there was a nerdy bone in their body in order to GET that nerdy bone in her body, OR, the female would snort, deride, or be passive about her request to play, being constantly socially aware of how she is perceived as a female in jr./sr. high and heaven forbid, the burping grunting drooling geek boys before her should think less or little of her for wanting to play a "boy's game." The question might sound something like "Really? Elves and dragons and trolls? Weird(potential code for wrong or stupid). How does that work?" Which translates to "that looks like fun, can I play?" But the boy's hear, "Your game is weird, tell me more so I can make fun of you and not have sex with you ever, and tell other girls to never have sex with you and tell the whole world (all two dozen people we know) how big of a retard you are (yes, retard, because we are all that mean we just learn to curb it, most of us.) The answer is would be something along the lines of "Here's the book," or maybe even "here, let me roll you a character" and then I know in our case her first and only session involves, "you see an elven female, wearing a cloak, boots, a sword and a smile," and the DM promptly gets slapped on the arm and she leaves.
That went off on a good tangent, not sure if it helped. The jist of it was, some of these guys were jerks and become bigger jerks and certain females are attracted to that much "confidence." Although I'm mostly speculating because I only knew two girls who had the slightest interest in participating, and I dated both of them. One moved 3 hours away and my friends didn't like her, and the other, we didn't hang out after we broke up and she had a different agenda in high school.
An actual scenario posited by Theatreg33k is that when they actually attempt to play they are left to their own devices much like guys do with guys, and if you ask for help more than three or four times OR you ask something more complex than "which die is that" the guys get frustrated and then she gets upset and then nobody had fun. I have done this myself, I feel like the biggest jerk ever, I say it's because I know how smart I believe she is and this is why I cant GM, group/raid lead in wow or watch her play video games. She also comments on how a girl changes the dynamic drastically. And it's not just girls, others have talked about, and I will probably too at some point, how one person can change a social situation by miles, doesn't matter. But specifically, dude's don't always know how to conduct themselves around a female friend or even one of their significant others and the "dick joke quota" drops drastically. Amazing insight, I know.
Let me get back to the original question, why would teenage boys say no to a teenage girl? More specifically, why they wouldn't let her play. It ties into the jerk complex above, where the girl just isn't invited. Or maybe adding a new player in the middle of a game who doesn't know the system at all can be a pain.
Oh teenage psycho-emotional issues, how you plague our lives. Remember guys, don't deny you want to have sex with your friend, just don't tell her every hour, and try to be friends with her first. If she wants to make out with you, it will probably happen. Unless she's an anime kid, then you have more problems, BUT fix them by watching anime.