Ideologies can't be stomped out. If that were the case, every -ism but humanism would've been stomped out right after their inception. This includes Islam. It's an ideology. Like every other religion known to mankind, it's a set of ideas masquerading as a political ideology wrapped in the cloak of Faith. Faith breeds hope. And as long as the followers of Muhammed have faith that they're ideology is the "right" one, it will continue to be fostered and spread about.

The only way to defeat an ideology is thru education. The problem is that education is a tool both sides use to promote their ideas that the other side is wrong. And as long as you have fools willing to buy into the ideology that Islam is the "end all, be all" of the Abrahamic Faiths, we will continue to have this debate.