Why Does The Church of Jesus Christ of Latter-day Saints send Missionaries to Christians?

Many people wonder why The Church of Jesus Christ of Latter-day Saints sends missionaries to teach Christians. Apparently, their assumption is that all that is needed to be happy is to know that Jesus Christ is the Son of God. Yes, that would is a great start, but would it answer major questions such as, "What is the purpose of life"? Does it teach them how to live here on earth, and how to return to live with Heavenly Father?

What if you had the answers to these questions and many more? Could you just sit there, smug in your knowledge, and not feel an obligation to share this great gift with others?