Animals have some adaptations in the teeth so that they do not need to brush. For eg. the teeth of snakes are very thin and sharp and usually curve backward. They are used for capturing the prey and not for chewing purpose. Snakes swallow their food whole. The carnivorous mammals (cats, dogs etc.) have more pointed teeth that are adapted to cutting and shearing. Chewing is not essential for them.
The herbivores need to chew their food (plants) to breakdown the cell wall. Although the teeth come into play, the nature of food is raw, ๏ฌbrous and non-sticky. So they also do not need to brush.
Humans use re๏ฌned diet that has readily fermentable carbohydrates that may cause dental caries and periodontal diseases. Also, many food items are soft and sticky. Therefore, in humans, brushing is essential.