Pedophilia as the scientists use the term is an attraction to prepubescent children. It is rare. Most straight men see a 6-year-old girl and do not feel any significant sexual interest.
What about 13-year-old girls? I will try to convince you in this post that the vast majority of ordinary straight men feel a strong gut-level sexual attraction to the average 13-year-old girl in the US today.
Why does it matter? The world is right to be deeply concerned about child sex abuse. But the vast majority of incidents that fall into that category concern girls aged 13 and older. In the public mind such abuse is the work of pedophiles. But it is not. What lies behind such incidents is not an unusual sexual attraction. What underlies them is not properly controlling the expression of an attraction. If there is any mental illness involved, it involves such things as impulse control or empathy. I am in no way arguing that sex with 13-year-olds ought to be legal or accepted.
The 2012 movie <"Are all men pedophiles?"> https://en.wikipedia.org/wiki/Are_All_Men_Pedophiles%3F made this basic point, except that they were misusing the term "pedophile". What it showed convincingly is that most men are attracted to girls of age 13 or older.
Note that in choosing who to actually date (or sleep with), much is taken into consideration beyond gut-level sexual attraction. When choosing a partner, men will typically consider a host of other variables that will make women roughly their age more attractive. One way to think about gut-level attraction is what enthusiastic partner you would most prefer going to bed with for an hour, never to see them again.
I am not claiming that men find 13-year-old girls to be the most attractive females around. Most will be more attracted to women of age 18 or older. However, the famous <OKCupid study>https://www.businessinsider.com/dataclysm-shows-men-are-attracted-to-women-in-their-20s-2014-10 shows that it is not much older than that. The only reason there are no numbers below 20 is that the design of the study did not allow for it.
There are other lines of evidence. "Barely legal" is one of the most popular categories of pornography, suggesting that without the law there would be great interest in the girls who are 16 or 17. People are dismayed that so many men watch illegal child pornography, and it is a good bet that many of them are ordinary men seeking video of girls of 14 or 15 -- not 6 or 7. In other times and places, it was common for girls to be married as soon as they had their first period, which could well have been at age 13 or so. No one ever called their husbands perverts for being able to consummate the marriage.
When it comes to social policy, it does not matter who a man finds to be most attractive, all that matters is whether he finds girls of that age to be attractive enough. If a man is dating a woman with a 13-year-old daughter, what matters is that he has plenty of sexual attraction. What holds him back is self-control, and if he finds himself drunk and alone with the girl, after they've both had (separate) big fights with the mother, there is danger. This will rarely happen with the woman's 6-year-old daughter.
For those who are still skeptical, I will put in another post the <ultimate challenge>.
So when we think about men and sexual activity with apparently willing 13-year-olds, we should be placing it in the same universe of other cases where there is questionable consent. Here we find the man who propositions his adult date insistently and repeatedly to the point where she gives in rather than continuing to refuse. Here we find the man who has just had a violent outburst, and while he isn't explicitly threatening violence if his date refuses sex, she dares not find out. Here we find the man with a date who is very drunk. Here we find the man who thinks his partner is 18, only to find out later that she is only 14. The fact that this last situation is not just possible but common underscores the point of this post. Often if we are shown a picture of that 14-year-old, we do NOT say, "Surely he's crazy -- no one could believe SHE is 18!"
I suppose some feminists will claim that the men who act in these ways with girls they believe to be 18 or older are not just evil but sick, suffering from a mental illness. But I think most of us would say the men are suffering deficits of self-control or empathy. We should have exactly the same feelings about a man who does sexual things with a girl he knows to be 13. Our thoughts about appropriate penalties and sex offender registry status should be similar.
There is another category to consider -- men who actively seek out girls of age 13 with the intention of doing sexual things with them. That introduces an element of premeditation. But it does not apply to the man and his girlfriend's 13-year-old daughter.
A message to women: These attractions are an integral part of the minds of the other half of humanity. Some men will deny it to you to keep the peace and/or seem politically correct, but deep down, that's the way it is.