Because we don’t like to have fun, that’s why! But seriously, Mormons don’t drink alcohol because it’s a commandment of God to members of the Mormon church. It all started when Joseph Smith, the founder of The Church of Jesus Christ of Latter-day Saints, received a revelation from God that has become known as the Word of Wisdom. In it, members of the church are advised to not drink alcohol, chew tobacco, drink hot drinks (understood to be coffee and tea), eat too much red meat (man, that one’s tough because I could eat steak every day), and to do other things related to physical health.
At first it wasn’t a commandment for the church members, it was “more of a guideline”. But later on it became a commandment and today church members can’t enter LDS temples or fully participate in certain church activities if they’re openly rebelling against it. That’s not to say some church members might not imbibe once in a while and keep it secret, but if they do then they’re going to hell. Just kidding, but if it were found out then they’d get called in by their church leaders who would try to help them stop drinking.