In my European country, the age of consent it 15 (or 13?), but it is also in the law that if the adult have a hierarchical/coercive power on the minor (parent, teacher, public servant, host/landlord, boss, probably other), the consent is automatically removed and this is pedophilia. It is the same in Spain, and I'd bet in Portugal.
The age of consent being this low is to avoid prosecuting 15-20 yo having sex with each other. Not for gross old men to coerce minors into having sex with them.
Why does minority/majority matter? Minors are considered inferior to majors. They can't vote, and can't decide most of their life by themselves (loans, bank account...). We consider it 'normal' for them to get yield at/beaten by their parents (and once upon a time, teachers). The _minimum_ society can do to make up for them is protecting them as much as it can. And that means protecting them from predators like Epstein or even Seinfeld.