Timothy Keller in his book "The Reason for God" answers the following question which is often thrown at Christians: "Is it arrogant to insist your religion is right and to convert others to it?"
Here is part of his answer:
"The noted religion scholar John Hick has written that once you become aware that there are many other equally intelligent and good people in the world who hold different beliefs from you and that you will not be able to convince them otherwise, then it is arrogant of you to continue to try and convert them or to hold your view to be the superior truth (The Myth of God Incarnate)
(But here) there is an inherent contradiction. Most people in the world don't hold to John Hick's view that all religions are equally valid, and many of them are equally as good and intelligent as he is, and unlikely to change their views. That would make the statement "all religious claims to ahve a better view of things are arrogant and wrong" to be, on its own terms, arrogant and wrong.
Many say that it is ethnocentric to claim that our religion is superior to others. Yet isn't that very statement ethnocentric? Most non-Western cultures have no problem saying that their culture and religion is best. The idea that it is wrong to do so is deeply rooted in Western traditions of self-criticism and individualism. To charge others with the "sin" of ethnocentrism is really a way od saying, "Our culture's approach to other cultures is superior to yours." We are then doing the very thing we forbid others to do."