The front differential on a rear wheal drive 4x4 is weaker
than the rear. It is made for light duty occasional use.
You are more likely to wear and strain it
if you chain up the front only. That is why instructions
say to chain up the primary drive axle.

I have had a 4x4 swap ends with chains on the front only.
Very scary.

Chains on the rear give better traction going uphill
and keep you straight on the downhill.