Humanity has been grappling with these questions throughout human history… And lest we get on our high horse and think this is unique to some other place, remember that during the Crusades and the Inquisition, people committed terrible deeds in the name of Christ. In our home country, slavery and Jim Crow all too often was justified in the name of Christ.
The President appears to be saying that both Christianity and Islam have been twisted and distorted for evil purposes. Just as the Crusades, the Inquisition and slavery are not true representatives of Christianity, so violent Islamists do not represent true Islam.
How do you reform a religious movement? By returning to the teachings and example of its founder and/or founding documents. In the case of Christianity you return to the teaching and example of Jesus and the witness of Scripture. For Islam you return to the teaching and example of Muhammad and the Quran.
There are at least three respects in which Islamist ideologies claim strong support from Islam - that is, from the Koran and Muhammad.
One is the intolerance and violence in the Islamic canon. The Koran states "Kill them / the polytheists wherever you can find them (Sura 9:5, 2:191). Muhammad, according to Islamic tradition, said “I have been sent with a sword in my hand to command people to worship Allah and associate no partners with him. I command you to belittle and subjugate those who disobey me …” He also said to his followers in Medina, "Kill any Jew who falls into your power." Following in Muhammad’s footsteps, one of Muhammad’s most revered companions and successors as leader of the Muslim community, the Caliph Umar, called upon the armies of Islam to fight non-Muslims until they surrender or convert, saying “If they refuse this, it is the sword without leniency.”
It will not do, in the face of many such statements found in the Koran and the traditions of Muhammad, to throw one’s hands up in the air and say there are also bad verses in the Bible. If Jesus Christ had said such things as Muhammad did, Christianity’s political theology would look very different today and medieval Christian Holy War theology – developed initially in response to the Islamic jihad – would have come into being as part of the birth-pangs of the religion, just as the doctrine of the Islamic jihad did in the history of Islam.
Islamist apologists find it relatively easy to win young Muslims over to their cause precisely because they have strong arguments at their disposal from the Koran and Muhammad’s example and teaching. Their threatening ideology is growing in influence because it is so readily supported by substantial religious foundations. Islamism may not be the only interpretation of Islam, but by any objective measure, it is open for Muslims to hold it, given what is in their canon.
Islamism is a valid interpretation of Islam, not in the sense that it is the only ‘correct’ or ‘true’ one, but because its core tenets find ready and obvious support in the Islamic canon, and they align with core principles of 1400 years of Islamic theology.
UPDATE: Mark Durie has written at length about the difference between Christianity and Islam in relation to violence.