Dunno the reason why this is, but for some reason you can't edit the parachute units.
There is a simple solution though...create an empty parachute - flying - and name it chute. Plop down your foot soldier, edit his init line, then add
this moveindriver chute
(where chute is what you named the empty parachute) and presto! Your guy will start the mission in the chute, with the loadout you wanted