Well, why I actually don't know about the game rule, I can tell you how it actually is in real life:
Jäger squads don't have APCs/IFVs. They are pure infantry. They are carted from A to B in 2-ton trucks (Unimog) but don't fight from these.
The same applies to the Gebirgsjäger (Alpine Rangers).
The German infantry type that _does_ have Pumas and/or Marders is called Panzergrenadiere -- mech infantry. And these are indeed organized in squads of six.
Very generally speaking, Grenadiere are for open ground where IFVs can operate effectively, and Jäger are for rugged terrain.