Why do the Mormons say they are God's chosen people?

Actually, this isn't really a belief of the Mormon people. Members of the Church of Jesus Christ of Latter-day Saints (the "Mormon" church) believe that God loves all people equally. They also believe that each person should be given a chance to hear and accept the Gospel of Jesus Christ, and all people are welcome to become Mormons if they choose to. Mormons are not taught that they are better or more favored than anyone else.

Most Mormons would say that they believe they are the people of God, but they do not believe that God 'chose' them over anyone else. Mormons believe that an individual chooses God, and by following Him they become His people.