I think the conflict is fairly straight forward. The Greasers are what many think are stereotypical hoodlums. We, however, meet Ponyboy right off the bat and realize something is different. This boy is articulate and sensitive. As we meet the rest of Pony's family and the other gang members, we see a dynamic that works very much like an extended family. The paradox exists in the sense that some of these boys may, like Dally, do bad things yet they are also good people. This is the essential paradox of human nature personified through this extended family of tough yet sensitive guys. As in life, not all conflicts resolve themselves. Pony still has growing pains, Johnny won't get better and Dally must work to keep the family together. And this is as it should be.