The religion started in the atmosphere of war. That vibe leaks out into the minds of Muslims of all kinds from moderate to the extremist even if it's indirect.
I recall being taught about the victories of Islamic conquests through the ages starting with the Muslim-Quraysh wars. In Islam, war is seen as a reality of human existence, and as a valid means to deal with perceived injustice, oppression, etc. Finally, martyrdom in Islam guarantees one into paradise...
The problem with Islam is that it's extremely malleable. You can pick and choose your sources, scholars and books and have an Islam of your own. Each one has their side, and accuses the other of taking things out of context, or having an incorrect understanding. Some Muslims make heavy use of the No true Scotsman fallacy.
The former allows one Muslim to basically slide on the scale, from a nominal Muslim to an member of ISIS. You just need someone convincing enough to show you a few prophetic traditions, sound charismatic enough and revive your faith in the religion.