Only soldiers detached with airborne units will attend jump school. MPs generally have no reason to maintain a jump qualification status, so the Army won't waste it's time or a slot on you going to jump school. They definitely don't just send everyone who signs up to parachute!
Other than Airborne infantry units (101st, 82nd, etc.), special operations (Rangers, SF, AF SpecTac), and a few specialties like airborne linguist or airborne medic will also go, but that is so they may detach with airborne units.
