Why do you have to spit out your gum before the extraction of DNA?

Gum should not affect a DNA test but if it did I would assume because of the bacteria/dna on the gum/gum wrapper.

The bacteria on the gum is the reason why. In the process of making gum, there are so many things that touch it that could mess up the results of the extraction. Even if it was machines that touched it, the ingredients from gum had to be touched by humans to create it.