Why do the socs and the greasers fight ?

I think that both of your points are valid. The Greasers and Socs live on separate areas of town divided by some railroad tracks. This gives each group their "turf". The Greasers have very little in the way of money or possessions. They come from a low socio-economic class. They resent the Socs for having everything and flaunting their material possessions. The Greasers are frequently targets of Socs when they (Greasers) are few in numbers. The Socs perceive the Greasers to be tough so they want to constantly prove themselves. They are also bored much of the time so conflict with Greasers becomes an outlet for all their teenage angst. Constant conflict gives both groups a sense of identity that they can feel proud of.