If you go out to eat and put your chewed up gum under the table, your server hates you. Guess what? Anyone who sits there after you hates you to because their hands accidentally brush up against a chewed up piece of gum, covered in your spit. Hopefully only your spit and it wasn't a shared piece of gum.
We have 49 tables where I work. I checked 42 of them because the other 7 were occupied. 8 of those 42 tables had gum underneath, despite having been checked last week.
Your server is the one who has to clean it up. We also don't like your nasty chewing up left on the side of your plate or glass. We have to scrape it off the plate before passing it to the dishwasher, who will look at the sticky remains and know it will have to be washed more than once to make sure it's all gone.
So what if we use cloth napkins?
Take your gum chewing nasty ass to the bathroom and throw it in the garbage, like you were taught to do as a child, asshole. There's a reason teachers never allowed gum in class and I am one piece away from starting a petition to ban it from restaurants too.
The only appropriate place for your gum is in a napkin, in the trash. Don't know where it is? Ask.
But do not, under any circumstances, leave that shit anywhere except a trash can when you leave the restaurant. Or I can promise you that every single person who comes in contact with it will hate you and wonder where your parents went wrong.