What was a cause of the Iraq-Iraq war?

There is no such thing as an Iraq-Iraq War.

Iran-Iraq War
If the question intends to ask about the Iran-Iraq War of 1980-1988, several causes of that war include:
  • Oil-rich regions along the border and access to the Persian Gulf.
  • Religion: Saddam Hussein was a Secular Sunni and Ruhollah Khomeini was a Fundamental (Usuli) Shiite
  • Government: Ba'athist State vs. Islamic Republic
  • Nationalism / Power
  • The two countries had a long history of border disputes, going right back to when the countries were the kingdoms of Mesopotamia (modern Iraq) and Persia (Iran).
  • Iraq wanted the new and unstable Iranian government to fall.
  • Saddam Hussein sought domination of the Middle East.
  • Radical Islam threatened to spread into Iraq from Iran.
  • Territorial disputes between Iran & Iraq.
  • Iraq was aiming to replace Iran as the dominant Persian Gulf state
  • Saddam Hussein wanted to annex the Ahwaz Arabs (who were under Persian Occupation in Iran)

Iraqi Insurgency
If the question intends to ask about the current Iraqi Insurgency, there are a vast number of reasons as to why Iraq boiled into Civil War when the United States arrived. Saddam Hussein had a very strong grip on the country and as soon as he was forced to let go, all of the different issues he had held at bay (through very autocratic and violent means) came to the fore.

1) Sunni-Shiite Conflict: The religious differences between Sunnis and Shiites (both variants of Islam in the same way that Orthodox and Catholic are variants of Christianity) are not terribly important for the purposes of understanding this conflict. The religions function as ethnic groups. The Shiites have been the majority population in Lower Mesopotamia for nearly 700 years but have never been in power. To keep power over them, the Sunnis repressed and tortured Shiites. The promise of democracy means that the Shiites would have power for the first time in Iraq's history and many Sunnis are scared of Shiite retribution, leading them to fight the Shiites to keep them repressed.

2) Mawali-Arab Conflict: The Mawali (non-Arab Muslims) in Iraq are quite numerous. The most famous group of Mawali in Iraq are the Kurds, but they are not alone. The Kurds have wanted to pull away from Iraq for a very long time and create an independent Kurdish State because of how horribly Saddam Hussein treated the Kurds. The Arabs, however, want to maintain the Kurdish regions of northern Iraq because they contain a number of Oil Fields and they do not want to instigate conflict with Turkey, which would oppose any independent Kurdish State. Kurds have also been incredibly supportive of the American Invasion and its respect for their lifestyle and Peshmerga (the Kurdish Militia). This has also engendered hatred from the Arabs on account of the Sentiment of Humiliation.

3) Sentiment of Humiliation: Iraqis see the United States as a Western occupying power not unlike the Colonial Empires of Britain and France which previously occupied the region. They feel humiliated that once again, they were unable to properly defend themselves and are at America's mercy. Some groups (like the Kurds and Christians) approve of the American presence, but most Arabs strongly disapprove of a continued American stay in Iraq and began to react violently to promote American withdrawal. Al Qaeda picked up on this sentiment and moved into Iraq to further foster jihadist reactions.

4) Muslim-Christian Conflict: This conflict is relatively one-sided since the Iraqi Christians have neither the facilities nor the disposition to violently engage the Iraqi Muslim population, but many Muslims in Iraq mistake Christians in Iraq for being in an alliance with the Christian American forces and European forces in general because of their friendship with the conquerors. The affability that Christians in the Arab World show Europeans is usually respect for the elimination of the Dhimmi Status and the Promotion of Equal Rights as opposed to being an indication of a long-standing political alliance. However, the mere notion of the fifth column brings many Iraqi Muslims to violence.

5) Localized Tribal Conflicts: Iraq is composed of numerous well-defined tribes. Each Iraqi (whether Arab or Mawali, Christian or Muslim) knows what tribe he belongs to by birth. These tribes regulate everything about a person from who he can talk to, to whom he can do business with, to what his faith must be, and even where he can live. Numerous different tribes compete over local resources and it is not uncommon that the bloodiest conflicts arise between two tribal elders from different tribes squabbling over three or four city blocks. Moqtada al-Sadr was probably the most famous tribal elder so inclined to use violence to solve his problems with neighboring tribes and the Americans.