While this a a few hundred years after the area I'm comfortable with, I do have many of the sources from this time at my finger tips with my post at the Academy of the Rose.

Some of it is easily answered by a knowledge of ji'e'toh, a balance of honor, ji and obligation, toh. The Aiel had toh toward the ruling line of Cairhien for offering the Daishan Aiel water during the breaking. Once the Aiel were able to discern who to repay now that they could, sadly after the death of the Jenn, they sent one of the last remaining Chora cuttings from what they called Avendesora, or the Tree of Life at the time. The Aiel presented Avendoraldera, the sapling of Avendesora to the Cairhienin royalty around 510NE.

This started a friendship that lasted centuries, allowing Cairhien the sole right to travel in the Waste. For centuries this propsered until King Laman decided he needed a new throne. He had Avendoraldera cut down and shaped into a throne.

To the Aiel, the Aiel War was not even a War, it was simply an act of toh. They needed to show the Cairhienins that there was no sin greater than destroying a priceless gift showing their friendship and alliance. To cut down the Avendoraldera was to break the alliance in the most insulting way possible with the Aiel.

They had no hatred toward the Westlands, only toward Laman and those who defended him. All of the fault can be placed on Laman, he fled from Palace to castle, fortress to fortress until he finally had shelter in the White Tower, where the siege and the famous Blood Snow occured.

If Laman had accepted his toh, then the entire War would have never happened. It was only a War to the Westlands, to the Aiel it was justice.