I like Ann. And have decided that I agree with conversion theory. However, Islam does not say or promise peace toward infidels when it talks about being a religion of peace. Here is a good definition of the meaning, and it shows what happens when one believes false doctrines. Things go haywire. From Gabriel Oussani: Grammatically, the word Islam is the infinitive of the so-called fourth verbal form of the regular intransitive stem salima, "to be safe", "to be secure", etc. In its second verbal form (sallama) it means "to make some one safe" and "to free", "to make secure", etc. In its third form (salama), it signifies "to make peace", or "to become at peace", i.e. to be reconciled". In its fourth form (aslama), the infinitive of which is islam, it acquires the sense of "to resign", "to submit oneself" or "to surrender".
Hence Islam, in its ethico-religious significance, means the "entire surrender of the will to God."
So the peace they are claiming is for themselves. Not to us.