So you are disagreeing that white European birthrates are below replacement levels or that the Muslim immigrant birthrate is much higher? How quickly do you suppose birthrates can turn around? Why else would Europeans decide to replace children with immigrants if not because they choose not to propagate their great culture? It can't be purely economical because no positive effect on the European economy is evident and the social effect is too negative.
Cultural relativism is an interesting mind game, but its easy to see where the problems lie. If Islamic culture was equal to Western European culture, then Pakistanis would be building space ships to land on the moons of Saturn rather than beheading homosexuals. These are the people you are letting in and expecting that magically they will share your ideology of tolerance and democracy just because they are in a different location.
These two videos are central to my views.
http://www.youtube.com/watch?v=ZDKk15KcqNk
http://www.youtube.com/watch?v=EbEpB3Q7vwk
First video describes the plan in detail. It is not covert or violent. It is preached in Mosques across Europe. If you say that this is just a small mentally handicapped minority of Muslims than there are two questions to answer.
1. What is happening in Europe that will make his plan not work? What is being done to battle Islamism (by which I mean political Islam: Fascist Theocracy) and promote secular European culture as better substitute for Islam? What will happen to these young Muslim men who reject education, their host country, and threaten to kill and hurt so casually? They will go on welfare, just like the 7/7 bombers. What makes them worth paying to keep in your countries?
2. Of all the talk of a large peaceful Muslim majority I ask, where are they? Are they protesting in the streets against terrorism and suicide bombing? Are they denouncing en masse the ideology of Sharia preached in mosques? Are they confronting the mobs in the street who chant about murdering the French or Belgian or Dutch? Would they stand up against a group of young Muslims beating an elderly white man? Why do they let a violent minority speak and act for them around the world? I think this supposed peaceful majority doesn't really care too much about the natives of their host country being hurt and killed, but they don't do it themselves. That's about as peaceful as Islamism gets.