I think the conflict is a matter of the combination of cultural traits and a strong sense of history.
If you take a cultural trait involving a tendency to believe that violence in defence of your people is not only right, but actually desireable, and add in a sense of history that has been handed down for generations, you get adults who have grown up hearing daily about the injustices visited on their ancestors by the people in the region next door.
That means a very short step to visiting the kind of violence on them that you have been educated to believe can, and will be visited on you, unless you do something practical to defend the rights of your people.
That - in a simplistic, but none the less valid scenario, encapsulates the conflict in the Middle East.