Semantics, indeed. I'm far too tired to reply in any sort of argumenative way, mainly because I think your points are valid and I would have to try to hard to play devil's advocate.
Good show, Zombie.
For the record, I agree with all your points, but enjoy arguing against convention for the sake of learning more about my own psychology through other people explaining theirs.
I think that is one of the few ways you can reliably learn about yourself. Always question why you have a problem with something.
As far as paedophilia goes, it's simply an attraction (sexual) to "children". Obviously, a grandma can perceive a 20 year old as a child and, thus, be a paedophile... This doesn't necessarily imply that the person goes out and has sex with this children, though. Paedophilia is both used to describe an attraction to children as well as molesting or engaging in sexual intercourse with children. I, personally, think this is a problem as some people are sexually turned on by cuteness. If you think a child is cute, then you may find yourself attracted to them for that reason. The problem with older individuals engaging in sexual intercourse with children (assuming that these "children" in question are sexually mature enough to not induce any biological problems with this) is that there is a skew of the power dynamic. It becomes very hard to tell if there is proper consent or forced consent. This can result in the development of psychological disorders as, if the age gap is significant enough, the younger party may come to see the older party as a parental figure. Intercourse with a parental figure is, generally speaking, not psychologically healthy nor biologically healthy as impregnation may result in dangerous mutations if they actually are your biological parent.
Socially speaking, the power dynamic and religion are the main reasons that there is an age limit to sex. Yes, it is arbitrary, but you will realize that it is often tied to the average minimum time people spend in schools. The general idea is that once you are out of high school, you should be equipped to have sex responsibly. Responsibly, in this case, pertains to what religious groups that permeate our culture want it to pertain to. It's a very sticky subject as most people look at it with a highly biased moral eye instead of a critical, logical eye. It really doesn't harm the developmental process to learn about anatomy as early as possible and to learn about sex as soon as you become interested in it. In fact, not being educated makes it more of a mysterious taboo that kids just want to explore as soon as possible.
In an odd, ironic way all of this control over sex is backfiring to make a more sexual society than ever. Maybe we'll go back to the times of the ancient Greeks... We'll all have orgies where we eat ourselves fat, drink ourselves stupid, and screw till we can't stand anymore. Wait a minute... People already do those anyway! Just not all at once! ;P Sometimes I worry about societies that prize morals over what actually works. Morals over truth... Always a sticky topic.