Their bodies can not metabolize it. Aspirin is fairly safe in most species. Compared to dogs, cats eliminate aspirin more slowly and are more apt to have side effects. Common adverse effects in cats and dogs include gastrointestinal irritation and altered platelet function. Buffered and enteric formulations of aspirin cause less GI irritation than plain aspirin.
Renal toxicity is uncommon.
Ketoprofen would be a safer alternative for cats. Etodolac was recently approved for osteoarthritis in dogs. The safety and efficacy of etodolac in dogs is comparable to carprofen. Potential adverse effects include vomiting, diarrhea and lethargy. Etodolac is not used in cats.