Islam doesn’t encourage peace or anything resembling it. It tells people to murder those who will not convert. It tells men that women and children are property. It tells men that any woman not dressed in a burqa AND escorted by a male relative is “just asking for it” and that a woman must have FOUR witnesses before she can charge a man with rape. It encourages murder as a way of salving ones family’s “honor”. It discourages civil behavior and encourages violence.
Re your tagline: what kind of being would make up such a religion and demand complete and utter subservience to it?
The “peace” to which they refer is the “peace” that exists after the entire world is subject to shari’a law.