Q: 3 of my 6 males have started to take bites out of their own tails in the last couple of days. They are in 1 gallon bowls arranged so they can see each other. Do bettas sometimes turn on themselves when they continuously see other bettas which they can't fight?
A: I never card my bettas so they see each other all day and flare at each other a lot. I have rarely seen any of them turn on their own tail. The fact that you mention 3 males all losing parts of their tails at about the same time spells trouble to me. I don't think we are looking at 'accidents' here, but rather at a pattern that looks a heck of a lot like fin rot to me!
You need to closely examine your bettas. Look for any color changes around the tear areas. Is the edge darker? Or perhaps reddish? Are the bettas fins healthy looking or do they look 'sticky' or 'stiff'. Is there a day to day progression of the fin tear (as in: is it getting a little bigger everyday). Any of the above would be a clear indication that an infection is getting your betta's fins. See fin rot.
Other possibility: Did you recently add plastic plants in those bettas bowls? If so, the bettas may be tearing their fins on the sharp or pointy edges/ends of the plastic plants leaves. Remove them and replace with plastic plants that have rounded leaves.
Last option: If your bettas are halfmoons, they may be blowing their tails. If they are pet store bettas, you have nothing to worry about (God knows LOL). It might be safer to card your halfmoon males if their finnage has become too heavy (hence too fragile).