Originally Posted by deltav

To me it looks like an anxiety or neurotic thing, lots of them chew on stuff like that. Maybe he had separation anxiety a couple years ago, now the habit's stuck or there's some other stressor going on. That is my guess.

My dog licks pillows when she's nervous, but she also does obsessive things with socks for no reason - secretly (she thinks) taking them out of my laundry hamper every day after breakfast, balling them up her in mouth, then hiding them somewhere. If you catch her and say what do you have there, she just drops it out of her mouth in mid-stride and keeps walking like "What sock?? I don't have a sock". Dogs are odd.