I also have heard allergies can cause them to bite or lick their paws.
I suggest looking closely at the health of the nails, are they splitting or separating?
My german shepard at about age 2, started constantly licking and biting his paws. His nails were actually separating from the quick and then breaking off. He was diagnosed with a nail disorder. We gave him medicines (one was an antibiotic) for quite a while and vitamin E, then tapered off the antibiotics.
At first the vet talked about removing all his nails, but after consulting with some colleagues, determined this course of treatment.
Our GS only takes the vitamin E now (and thankfully still has his nails). Not knowing what tripped the original condiition, I am very caution of allergens -- just in case. We keep the nails trimmed short and a close eye on them.
(And Sandy, we 're with you, he absoutely hates having them trimmed. The vet does it and he is muzzled (the dog, not the vet).