is pedophilia common?

One of the big things on social media today is outing self-loathing, conservative, gay homophobes.
Is the new thing the shouting from the rooftops self-loathing pedophile?
The assertion is that "most" men are pedophiles. Honestly, reading up on the subject of pedophilia for the past several years, I've also come to this conclusion. The problem is that society shuns such feelings.
Men have many "problems" that no longer fit modern norms. The biggest problem is aggression. According to Stephen Hawking:

"The human failing I would most like to correct is aggression. It may have had survival advantage in caveman days, to get more food, territory or a partner with whom to reproduce, but now it threatens to destroy us all."

Carl Sagan said:
"In the long run, the aggressive civilizations destroy themselves, almost always.”

So, if "all" men secretly are attracted to little girls, are they pedophiles who are only attracted to little girls? Or are they more omni sexual? As such, do they have sex with any available female because little girls are taboo?

So many questions. So few answer.