It's not as clear cut as that, I'm afraid. And it goes back to before the first world war. If you want to dig deeper into it, it goes back centuries. Within the Islamic Empire there were forces pushing for radicalization and forces pushing for westernization, even before the rise of Western Empires that happened in the 19th century.
It's easy to put the responsibility for this outcome solely on the west, but it ignores the fact that Islam was sinking from its enlightened heights of the 14th century even as America was yet to be colonized.
It ignores the fact that Islamic Empires attempted to conquer Europe in the 17th century and were almost successful in doing so. They reached as far as Vienna before they were pushed back, and the cultural influence that had on the west was probably an unforseen consequence, from the point of view of the ruling powers of the time.
It ignores the Islamic slave trade which was of larger scale (iirc) and longer duration than the European and American ones. It ignores the fact that Muslim terrorism by non state actors (that was secretly indirectly funded by Islamic states) is not a new invention either, and was practiced at least as far back as the 18th or 17th centuries.
There's a ton of history we don't learn about and much of it has to do with the empires that came before the west.