Perhaps some straight male readers will scoff at the idea that they have any attraction at all to 13-year-old girls. Warning: various people might find this post to have arousing elements to it. For my purposes, this is unavoidable.
Here is a thought experiment. It is a few years from now, and based on your 23AndMe profile, scientists contact you with a proposition. Due to your genetics, you are the only known person on earth who can cure a 13-year-old girl of a fatal illness. She looks perfectly normal now, but if it isn't treated she will rapidly go downhill and die within a year. What you must do is to have sexual intercourse with her. She confessed that she's been fascinated by the idea of sex for a couple years now and looked forward with ambivalence to when she could try it out. They showed her your picture before and she blushed while saying she'd be happy to sleep with you anyway, even if it wasn't to save her life. Given what's at stake, she's downright eager. The doctors have arranged a legal waiver because of the circumstances.
It turns out she's pretty nice looking for a 13-year-old. Do a Google image search on "13-year-old girl models". Those typically show you only faces, but with a little effort you can find pictures of their bodies too. Try an image search on "middle school gymnastics teams" and look at the ones with faces or body shapes you find most appealing. Others who are better at searching can find better images -- but please, don't seek out anything illegal!
So, you're a good Samaritan and you figure you'll give it a try, but you're worried about whether you'll be able to get it up. So here you are with her in bed. She's naked. Her breasts are not adult size but they are most definitely there. There's a tuft of pubic hair, though not as much as adult women have. With a smile she spreads her legs and gently spreads her labia. You can see it's wet inside. She confesses with a giggle that she's been masturbating, wanting to be as ready as she can be. She's used full-size dildos before so there will be no pain. She's got a Plan B ready to take after it's over just to make sure she doesn't get pregnant.
She looks at your penis with a mischievous smile, and gently cradles it in her fingers, then rubs it gently. Look again at that picture of your favorite model's face, then the girl on the gymnastics team, and imagine you are actually in bed with her naked. To save her life, you must have enthusiastic sexual intercourse with her and deposit semen inside her vagina. She looks at you with a warm smile, lies back, spreads her legs and labia and says, "Please?"
Is your penis soft?
Now let's compare this to what happens if the 23andme scientists find other people who need the same cure. You're pretty clear you would get it up for a lovely 25-year-old woman. But here is a 90-year-old woman (images await...). Here's a 20-year-old man (for whom anal intercourse is the treatment).
Now, if you hear of a man who did have sexual intercourse with a girl that age, was his problem one of self-control, or an unthinkable sick attraction?
Warning: If you have discovered an attraction, let me remind you that you must never, ever engage in any sexual activity with actual girls this age. It's illegal and risks serious emotional damage to the girl, even if she were to appear willing.
<This post> describes the larger context for why this question is important.