Okay, sit down, and let me elaborate on why this is a bad idea.
I was going to post a kneejerk reaction, namely "This idea is bad and you should feel bad", but that wouldn't help the discussion.
So let me assume you mean the best. Let me assume you want to encourage a better gender balance. And let me tell you that this is a terrible way to go about it.
Aside from the points elaborated in other comments -- and let me stress the "industry rife with sexism, inequality, and bro-culture rudeness" -- this flies in the face of the hacker ethic. To wit:
* Hackers should be judged by their hacking, not criteria such as degrees, age, race, sex, or position
Now, I can hear the defense mechanism riling up right now: "But wait," you say, "we're not judging participants based on their gender, we're just teaming them up that way. The judging will be fair!" And I believe you believe that, with the best of intentions. Nonetheless, you've automatically broken the blindness and impartiality of the judges, simply because they know that it's an uneven distribution. Think of it like a scientific experiment where everyone knows where the placebo is. It doesn't matter who wins; everyone loses, because one side will claim the other got some special consideration. Imagine if you did the same thing, only with college-grads vs. self-taught hackers. If the judge is from Stanford, you lose.
At best, this will fizzle, or go off unremarkably. At worst, you're actively making worse exactly the problem you're trying to fix. At best, this is a trite idea ('boys vs girls' is overdone, schoolyard, and simplistic). At worst, it's actively discriminatory.
Be more creative. You recognize a problem, but this isn't the answer.