I'm a pagan now, of course, but I still understand the literature and philosophy pretty well.
38 "You have heard that it was said, 'Eye for eye, and tooth for tooth.'
39 But I tell you, Do not resist an evil person. If someone strikes you on the right cheek, turn to him the other also.
This eye for an eye business has no place in civilized society. You can only ever hope to make enemies. Christianity is supposed to be about peace. At least that's how Constantine and the Holy Roman Empire sold it. Do not resist an "evil" person. If you return aggression with aggression you will only ever get aggression. So, let it go.
40 And if someone wants to sue you and take your tunic, let him have your cloak as well.
Obviously, if someone want to sue you and take your tunic, they are very needy so you should give him your cloak, as well. There is plenty, and there is no need to hoard anything. If you want others to realize this, you have to behave as if you also believe it. Therefore, hoard nothing - give freely.
41 If someone forces you to go one mile, go with him two miles.
This piece, I think, is allegorical to having patience. You go "with him" two miles, be patient and listen to understand why a man would "force" you to walk a mile. It serves you also, you will learn what to do and what not to, if you listen accepting that the other person has reasons for doing the things that impinge upon your enjoyment of life.
42 Give to the one who asks you, and do not turn away from the one who wants to borrow from you.
This is again in regard to the hoarding that humans do. No matter how often we say it is better to give, we still hoard more than we need, and the whole world is impoverished for it.
A man acts in the interest of survival for himself and his family, based upon knowledge he has about how to survive. If you want men to act differently, you have to teach them that changing their actions improves their chance of long-term survival.
The Bible, IMO, tries to tell this in several ways - the whole forgive everyone for everything, do unto others as you would have done unto you, and do not judge others - leave the judgment to god is trying to tell men how to have "more life," but too many Christians simply don't learn this from the myths and histories therein. Jesus was a pacifist. You cannot truly "defend" yourself from ideas, you can only propose new and different ideas. A lawyer doesn't simply refute charges, he paints a different picture of the situation for the jury.
Jesus himself may have never existed. There are no extra-Christian texts making reference to him. The miracles, and the ascension would have probably gotten some attention from the scholars at the time, but texts referencing these things have not yet been found. You can come to your own conclusions therefrom. Constantine used Christianity (a small mostly Egyptian cult at the time) to further his quest for world dominance, so there are a lot of contradictions in the literature that leave one scratching their head.