It most certainly does agitate them. So that is certainly amongst a host of motives. I believe they really don't need this, nor any excuse, since for them, any excuse will do. Islamist violence against infidels is imprinted into their DNA.
It's an historically indefensible position. Islamists have been attacking non-Islamists since they crawled out of the slime for one reason: the Satanic handbook delivered by their murderous prophet compels them to. They have a religious duty to be an existential threat to western civilization.
Well, it certainly is a defensible position. However, "they attack us because we are over there attacking them" is only part of the equation. The rest, I am convinced, is like you offer. They are guided by Satan's handbook requiring them to convert, enslave, and/or murder all infidels.
Perpetual no-win "wars" ensure that the bureaucrats in charge have lifetime job security.