What Westerners don't always grasp is the fact that, unlike the average Christian believer, for whom their faith is a part of their life, for an estremely devout Muslim, their faith is their life, it is intriniscally woven into who they are.
If a Westerner converts to this extreme version of the Muslim faith, then they genuinely see their role is to fight and die for that faith, and that is something they embrace and are excited to show their devotion.
So the battle is not 'someone else's', as emmie states, it is seen by these extreme devotees as a battle for every Muslim, and every Muslim should be not only willing, but actively seeking an opportunity to fight and die in the Jihad.
Not something I would envisage, but I am not a believer in any religion, so I would never experience that level of fervour, but I accept that others do - even though I think the consequences do not achieve their aim, or what I understand Allah would want.