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The original idea of worldly peace in islam comes from uniting warring tribes under one banner, which from the very beginning was NOT a peaceful act. Islam spread by conquest and bloodshed. Muslim nations and groups have always fought each other. It is a hypotethical peace which is never achieved.
The prophet himself fought. Right after his death fighting began among his followers. The porphet's family and people who knew him (the sahabe) were killed and their city burned by the guy whose lineage took on the leadership of islam. It'd be more accurate to say that islam is a religion of war.
Of the abrahamic religions, islam is the only one where the prophet himself is known to have killed many people (for whatever reason but mostly to spread islam, or "peace").
The prophet Muhammad and the Koran support the idea that women should be treated as property subservient to men, should cover themselves as to not tempt men, 50+ year old men can take and rape 9 year old wives, that infidels should be murdered, and spefically speak against peace with infidels.
Teachings in islam do preach for violence and war in some instances, which nullify islam to be exclusively peaceful.
There have been no proofs where Islamic authorities have intervened in a helpful manner against terrorism, the way they took up to Charlie Hebdo. Selective mutism.
There are radical elements in most religions, radical Muslims dont represent Islam as a whole.
Islam is a religion of internal peace. They are peaceful to each other only, not those of any other religion.
The Qur'an itself states that violence is usually only permitted in the context of some form of self defense.