Nelson (current head of the church) just doesn't like the word and wants to change it. Confusion, inconvenience, and Pragmatism be damned. It's his right as prophet to say that Jesus told him to use the full name of the church and drop Mormon, but let's not pretend it's suddenly offensive because it's been used by enemies of the church. They've also used the full name as well, so that should be offensive if we're staying consistent.
More reasonably, I think they are not offended. Rather they are simply trying to use the full name of the church rather than any sort of shortenings. Sure, if somebody was being a jerk and using the word Mormon to be a jerk, then that could be offensive. However, that's a much different thing than being offended by the word itself used in a friendly context.