"Christian" originated as a demeaning term, intended to mock people who followed Jesus or Jesus' teachings. It'd be the equivalent of me calling someone who posts a bunch of pictures of their butt on the Internet a "little Kardashian". Christians who were first given the title saw it as a good thing, of course, since the meaning was basically someone attempting to act like Jesus.
Mormons are pretty open when it comes to taking about their faith, so if you don't understand why they use that title, maybe you should just ask them in what way they try to emulate Christ. I'm sure they'd answer that one for you.
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"Mormon" began as a title of persecution also, just like "christian". When the church began in the 1830's, we were just "Christians" and "latter-day saints", eventually though people starting calling us "Mormons" as a slur. Slurs have been used throughout history to dehumanize people you don't agree with and/or hate. It is unfortunate but it happens. We are ok with the title "mormon" now a days. It should be noted that we were accepted as a christian faith until about the 1950's and the rise of evangelism. Heretical of course but accepted. Again, it is my faith is Jesus that makes me a christian. I could care less about being accepted into the "christian club". Let me define who I am, by my faith and my works. God Bless.