Let's presume you are right and that a disturbingly large, statistically significant proportion of society are in fact pedophiles.
How are you combating the largest source of sexual abuse: i.e., family and friends? And why is that not applicable to your child's education where their risk factors are far lower?
I don't know about you - but I'm not going to ban my neighbors from seeing my child, nor would I give Uncle Bob the stink eye every time he gets near my niece. The reasonable stance in this case seems to be one of vigilance and education - be mindful that it may happen, educate your child to report untoward things, and do your best to vet people close to you.
You do this for your babysitter too. So why not your educators?
Your concerns are valid, but IMHO your reaction is entirely disproportionate. If your stance is proportionate to risk, you wouldn't ever leave your child alone with a family friend, or your own siblings for that matter. It still seems unreasonable to ban an entire gender of educators from your child's life over this.
To be clear, I'm not trying to dismiss your concerns in their entirety (though I do question the weight of these concerns). What seems absurd is that most families fail to address the far larger, far scarier risk factor while devoting all of their attention to a relatively tiny slice of the child abuse pie. It also seems absurd that these same families are willing to throw male educators to the wolves while Sketchy Uncle Bob gets a free pass.
[edit] As an aside:
> "studies show that women commit 14% to 40% of offenses reported against boys"
That's a gapingly wide confidence interval there. What sort of data are we basing this on?