[Technical question] Why would damage occur when being towed?

[JCL]

Originally Posted by autoque

Ah~, so it wouldn't be advisable to go down hill in neutral even with the ignition on. I liked doing that 'cause I thought it saves some fuel while doing so. Never did I think it could damage the transmission and transfer case.
I'll use neutral only when going through the car wash tunnel from now on.

I'll skip the car wash comments, since I use them too (touchless though)

Coasting in neutral down a hill won't save you any significant amount of fuel, since the fuel injection cuts fuel flow on over-run. You are also adding wear to your transmission, as noted above. It won't affect your transfer case, since the transfer case doesn't know the difference.

More importantly, it is unsafe. You have three types of control of your vehicle; steering, braking, and acceleration. Putting the vehicle in neutral while moving takes away the last one of those, acceleration, if you have an impending accident. That is the reason it is also illegal in most jurisdictions (not sure about your state).