Your dog may not like having his mouth poked and prodded, especially if he has sore teeth or gums. Your dog may also not like the taste of doggy toothpaste that you or someone else has used in the past. You can work with your dog to acclimatize him to the process of having his mouth handled, and eventually his teeth brushed, so that even a stubborn dog will tolerate the process. Try different products such as dog toothbrushes, gauze wrapped around your finger, and different toothpastes, some of which are unflavored and others that have dog-friendly flavors like chicken or beef. If your dog is very resistant you may want to consider checking with a veterinarian to ensure that your dog is not experiencing oral pain from an oral medical condition.
Brushing a stubborn dog's mouth can be a real chore. An uncooperative dog can make tooth brushing unpleasant for everyone concerned Working to get your dog used to having his mouth handled, using a finger with a cloth or gauze to start, and using good tasting doggy toothpaste is usually successful in eventually getting cooperation from your stubborn dog.