This is a culture-dependent claim. In modern advanced societies we are keeping our offspring childish for longer than in historical or less-developed ones. I take it that by 'kid' you mean 'child' in the cultural sense, rather than in the biological sense, since most 13-year-olds are sexually mature (in the sense of biologically fertile). We advanced moderns have the luxury of being able to distinguish between these two senses, and I'm afraid people sometimes exploit that by glossing over the distinction.
Some 13-year-olds are childish; others are not. I don't think it's useful to use the same label for adults who have sex with them irrespective of their individual level of maturity. Your reference to rape seems to imply that 13-year-olds are incapable of giving consent, which I would disagree with.
No, but what would you say if someone claimed to be a non-pervert who'd had sex with a 13-year-old? My guess is that your concept of perversion is, as above, culture-specific: perversion is behaviour that is regarded as unacceptable by most people in your culture. But in the culture of, say, Anglo-Saxon England (which was one of the most advanced of its time in the world), it was perfectly normal for 13-year-old women (which is how they were regarded) to be married and pregnant. Indeed, in prehistoric times it was absolutely necessary for people to be procreating by that age. That's because life expectancy was too low for people to wait any longer if they wanted to raise their kids to adulthood before they died. And we haven't had time since then to evolve significantly different sexual natures, so having sex with the average 13-year-old is certainly not a perversion of nature.