Why keep our tickets stub

You should just in case you are asked while in the theatre to provide proof of purchase. It's not a terrible idea. As for keeping your stub after your movie, Chippewa Bowl (across Chippewa Ave from AMC Movies 16) used to offer a free game of bowling when you bought a game and presented your stub to them. I'm not sure if they still do.

Did they ask you to? I often keep ours for sentimental reasons but I cant think of any other reason...