It is not appropriate to hold a cat by its legs. Cats have delicate bones and joints, and holding them by their legs can cause them stress and discomfort. It can also lead to injury if the cat tries to struggle or wriggle free. Instead of holding a cat by its legs, it is better to support its body and hold it gently. If you need to handle a cat for some reason, such as administering medication or taking it to the vet, it is best to use a carrier or a blanket to wrap the cat in to keep it calm and secure. It is also important to approach and handle a cat in a calm and gentle manner, as this will help to reduce stress and keep the cat relaxed.