There are interesting questions here, however, beyond what has already been noted:
1. When was the rug in question purchased by the landlord? That is, how old is the carpet?
2. How much of the total carpeting in the apartment was damaged?
3. Can the damage be repaired? If so, at what cost?
4. Assuming all the carpeting is destroyed, what is the "value" of that loss? Examples might be: Original cost less depreciation, or replacement cost?
5. If original cost or even replacement cost, less depreciation, how is the depreciation calculated? That is, a brand-new carpet, merely because it is put into a given apartment, may depreciate 30% to 50% the very first year. What is the useful life of a carpet? Are there statistics or honorable resources that can provide guidance here?
6. Perhaps a good tip for readers here would be to always consider "renters" insurance...and learn about what the policy covers and does not cover. Personal liability should be covered and perhaps damage done by pets would also be covered. In some cases, landlords are the ones pushing this kind of insurance for tenants so as to avoid the type of dispute you will be involved with.