What political system did European countries set up that cause conflicts in the middle east?

In general, this is called Imperialism or Colonialism. Specifically, there are a variety of political issues that Europeans built into Middle Eastern Politics with the intent of or that directly caused conflicts:

1) Mandates: The European powers instituted a Mandate System which carved up the Middle East into colony like pieces of land that were based primarily on what territories each colonizer wanted and had little regard for the indigenous population.

2) Ethnic Mixing: The European Powers intentionally broke up large ethnic groups to prevent them from rising up against the Colonial Infrastructure and put ethnic groups that despise one another under the same authority in order for each to keep the other in check. While Europe was becoming more nationalist, they were actively trying to prevent this in the Middle East.

3) Foreign Appointments: Many leadership positions (such as the Kingship of Jordan, Egypt, and Iraq) were given as favors to Arab Sheikhs who were foreigners in the lands that they ruled. Their power was a gift from the European Powers and made their authority completely dependent on Europe as opposed to endemic support from the people. Until the Iraqi and Egyptian kings were overthrown, the people in these countries felt that their rulers did not represent their values.