In Australian rules football, throwing, per se, isn't allowed: The ball must be tapped with an open hand, or hit with a clenched hand or a foot. It's a dangerous motion when performed by a beginner near a lamp, but that appears to be what Obama did on Monday.
Coincidentally, "the football" also refers to the briefcase full of nuclear codes, which presidents possess. That kind isn't supposed to be thrown either.
credit: White House photographer Pete Souza