Nicklance, training and experience doesn't grant you DR. Training and experience would teach you how to avoid attacks, and that's represented by AC. DR, on the other hand, represents one's ability to take a hit.
An angels DR comes from its own supernatural nature: it is an outsider with the Good subtype. Good, in D&D, is a lot like a special substance. Things can be made of good. Angels have DR because of that very reason; they are made of supernatural goodness and so ordinary weapons aren't as much of a threat to them. Evil bypasses it because an evil-aligned magic item or creature with the Evil subtype literally contains Evil in it. Evil is the opposite of good, and so counters the properties of the Good inside an angel. In fact, it has nothing to do with evil people at all, just with that magical substance: an outsider with the Evil subtype (demons, etc) that is Good-aligned and was raised and trained by celestial beings would still bypass DR/evil, heck, a good-aligned mortal with an Evil-aligned magic item would bypass it too.
By the way, the angel has a +4 bonus on AC and a +4 bonus on saves against evil outsiders, so it's give-and-take. The one most advantaged by the Angel's rules is a normal person who has an Evil weapon, which makes sense: just like holy weapons work better against demons, unholy ones work better against angels.
