What's the main conflict (this could only be "one" as stated by my teacher) in the novel, "The Outsiders"? I know it's one of these three: person...

Your teacher definitely gave you a hard question to answer.  The three conflicts that you have identified are the three major conflicts that are present in the story.  I do not believe one of those is any more central to the story than the other two.  I think that your teacher wants you to pick one and defend your choice with reasons.  

I would choose Pony vs. self or Greasers vs. Socs.  I think those are more easily defended.  Between those two, I would choose the Greasers vs. the Socs, because there are many events throughout the book that you could use as evidence.  The rumble, Johnny's beating, Johnny killing the Soc, etc. are all events that support the gang conflict.  

The major conflict within a novel is often foreshadowed too.  Pony being jumped in the beginning and the flashback to Johnny's beating both focus the reader's attention on the gang war and culminating rumble.  They don't focus attention on Pony's personal struggles.