I find it really disrespectful when people chew gum around other people. I have no issue if people chew it in their own time, or at home or something, but it's just plain disgusting around other people. People seem to think they are quiet when they chew gum... but they aren't, they really aren't.
Not only does it look gross, but the chewing of gum produces the most disgusting, squelching sounds I think a human can make. When people are chewing gum on a bus surrounded by other people, or in a classroom with other students all around them or something I consider that very rude. I can usually put in headphones to block out the sound, but sometimes I can't and it makes me feel sick. The only other sound I can compare it to is when my dog used to lick, suck and chew on his paws in old age. It used to drive me crazy when he did that too. It's basically the exact same sound.
I personally never chew gum. I don't see the point of chewing some little plasticy thing around for hours that you can't even eat, and if you do swallow it's bad for you.
I also think there's a special place in hell for people who stick gum on the bottom of tables, seats, the floor etc for other people to then stand in or get it stuck on them in some way.