Why is the bounce at the bottom of the squat encouraged while the bounce off the chest in the bench press discouraged?
You bounce with momentum from your hips, which is athletic in nature. Bouncin from your knees is gay and will hurt you. In competition you aren't allowed to "bounce" out of the squat (usually) just like the bench rule is. Some people "bounce" off the chest but not in competition. Some think it'll physically hurt you but I don't believe that unless you're using major, major weight.
Which people tend to use in competitions.
You can't bounce the bar off your chest in competition. You must be able to bench when the command "press" is given once the bar touches your chest.
I wouldn't encourage anyone to bounce out of any movement sans maybe the olympic lifts.