Is DEET harmful to cats? Of course it is! Giving it to a cat is practically killing it.
DEET is a common insecticide primarily used to kill mosquitoes, bees, and other insects. While relatively safe, DEET is a deadly poison for cats. If your cat ingests DEET or it comes into direct skin contact with it, it can cause serious consequences, including vomiting, diarrhea, muscle spasms, difficulty breathing, poisoning, and even death. 
The severity of these reactions is dose-dependent, so you must be very careful to prevent your cat from being exposed to DEET. This is especially important if you have an outdoor cat. To keep your cat healthy and safe, use flea and tick treatments that are safe for both humans and pets.
If you are unsure whether your cat has been exposed to DEET, seek veterinary care immediately. The veterinarian will advise on how to treat different levels of poisoning. Therefore, to avoid the harm of DEET to your cat, you can consider using safe alternatives or other mosquito repellent measures, such as mosquito repellent patches or electronic mosquito repellent devices. Regardless of the method used, always prioritize your cat's health and safety.