Why is the dove the symbol of peace?

In Judaism, Christianity, and Islam a white dove is generally a sign for peace. The Torah, The Old Testament and The Koran describe a story in which a dove was released by Noah after the Great Flood in order to find land. The dove came back carrying an olive branch in its beak, telling Noah that the Great Flood had receded and there was land once again for Man. (Genesis 8:11).

I believe the white dove to represent purity and innocence as white it often associated with this