I'm assuming we are talking about Subaru after the time where it went from 4WD where you could switch back and forth to more modern times where the car is all time AWD.
The AWD platform is full time because it is designed to give power to all 4 wheels at all times for safety and performance. Subaru Symmetrical AWD is designed for balance, safety and performance in mind. Vehicles that have active AWD (where it only sends power to the other set of wheel when it detects slippage) are unbalanced because they are 2WD platforms with extra parts added to send power to the other wheels. Also, those platforms can not send much of the power to the other wheels, usually 10-20% maximum. They also have uneven axels from the extra parts, thus causing torque steer.
Subaru's goal of a Symmetrical, full time AWD is to have balance, a good distribution of power to all wheels at all times, and even axels. To have a system that is 2WD and can change to 4WD compromises these promises. This is why Subaru is the authority and leading seller of AWD.
All Subarus, not just the Forester, are "all wheel drive".
The 2010 Subaru Tribeca has all wheel drive.
The 2004 Subaru Forester has all wheel drive.
The 2008 Subaru Outback has all wheel drive.
The 2005 Subaru Outback has all wheel drive.
The 2002 Subaru Forester has all wheel drive.
The 2004 Subaru Legacy has all wheel drive.
The 2010 Subaru Outback has all wheel drive.
The 2001 Subaru Forester has all wheel drive.
The 2013 Subaru Impreza has all wheel drive.
The 2002 Subaru Outback has all wheel drive.
The 2007 Subaru Forester has all wheel drive.