And does it go the other way? Do you create violent anti-Islamists when Muslims commit terror attacks? Were the orphans of 9/11 more likely to sign up for the US military, or commit hate crimes against Muslims than their non-directly-affected peers?
Yes, of course it does. Hell, even on the recent 9/11 HN thread there were people who said they joined the military after the towers collapsed. It's only natural reaction when your nation gets attacked, and it works the same everywhere.
It's best to think of this as a single self-perpetuating process, with a strong feedback loop of hate and suffering inside. So the US bombs some Muslim countries, and eventually some group manages to pull off a 9/11 in retaliation. US reacts to this by utterly destroying several countries, and in reaction, ISIS is born. Which then US and others attempt to bomb out of existence. Rinse, lather, repeat. A kills B's people, B retaliates by killing A's people, A retaliates to retaliation by killing B's people, ...
Jihadists aren’t in a loop. That’s a myth. Jihad is real to them, and they are attacking non believers.
The stated motivation for the 9/11 attacks were the presence of U.S. airbases in Saudi Arabia. Not revenge for some past hurt or attack.
Why does everyone presume that what they say isn’t what they mean?
This is how religion is used to get people to do things. You can read anything you like from a religious book; you'll find justification for anything if you comb for quotes enough. This makes religion a glue, or an amplifier, not a prescriber of behavior.
Consider Christianity - the religion that gave us half of what's nice about the Western culture. That same religion using that same, unchanging book, set half of Europe aflame multiple times, for ostensibly religious reasons. When you look at it from outside it looks ridiculous, and when you study history you discover obvious political goals behind the crusades and other European wars - but then, a lot of people fighting and directing forces believed they do it because "God commands it".
It's no different with Islam. Jihad is just an excuse to get people to fight and die for political causes. If the political reasons disappear, they'll soon find an excuse to not fight, and Jihad will again become "the internal struggle".