I would have thought that the answer had become obvious, but apparently not. So let's answer.
In classical Islam, the world is divided into two realms, Dar al-Islam (the House of Islam) and Dar al-Harb (or Harab) the House of War. In brief, Dar al-Islam is any Islamic country that is based on Sharia law and Dar al-Harb is the rest of the world. As Wikipedia summarizes:
Dar al-Harab is a term classically referring to those countries where the Muslim law is not in force, in the matter of worship and the protection of the faithful and dhimmis. It is unclean by definition, and will not become clean until annexed to the House of Peace. Its denizens are either to be converted, killed or, if people of the book, tolerated as long as they pay the jizya.And those against them must be subjugated or killed. That war is one of the major definitions of jihad.
It is really that simple. They try to kill us because they are commanded to wage war on us until every country becomes Muslim.
Now there is some important historical context.
Over the past several hundred years there has been some watering down of the concept of Dar al-Harb, There have been new divisions added over time from the original two. Dar al-Hudna are lands that Muslims lands have a truce with; Dar al-Ahd are lands that have a treaty with Muslim lands; and Dar al-Amn arelands where Muslims are a minority but can practice their religion. But the critical fact about these new concepts is that they were created in order for Muslims to deal with the idea that they cannot take over the world as they intended. Their ultimate victory is not as axiomatic as they thought it was. In other words, as Islamic expansion ended and the West eclipsed the Islamic world militarily, economically and culturally,, the traditional concept of Dar al-Harb became weakened in order to accommodate the new reality where Muslims could no longer expect to realistically regard their domination of the world as inevitable.
Defeating Islam succeeded in making mainstream Islam more moderate.
But to fundamentalists, the old division of the world into two parts is still the only proper interpretation of Islam and the more modern, realistic Muslims are just as much the enemy as the West. In addition, the West's ascension is a reminder that the original intent of Islam to take over the world has been stopped and reversed. This is a source of intense shame, and that shame must be excised. The newer interpretations of Dar-al Harb was a way to reduce shame, but it was a cheat to those who believe that Islam is inviolable.
That is why they hate us.
ISIS is just the newest manifestation of Islamic terror groups that are based on the fundamentalist reading of the religion. There are scores of groups who want to re-establish the caliphate and who want to subjugate, convert or kill all non-Muslims. Most of them are more pragmatic than ISIS but the dream of a pan-Muslim caliphate still exerts a strong hold on the larger Muslim world, with 2/3 of those in Egypt, Morocco, Indonesia and Pakistan saying they favor the idea in 2007. Mainstream Muslims might understand that they are weaker than the West, but they still long for things to change,. The honor/shame dynamic is as strong as ever, and combining the longing for a strong caliphate to counter the West with the shame in the knowledge that the West is more powerful results in a steady stream of new recruits to ISIS that simply will not stop any time soon.
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