Hello, Annlu, and welcome to the Grammar Exchange.
Which one is correct using favorite and why?
1. My favorite animal is dogs.
2. My favorite animal is a dog.
3. My favorite animal is the dog.
Sentence (1) doesn't work, but you can say, "My favorite animals are dogs." The reason that (1) doesn't work like "My favorite fruit is apples," which is acceptable, is that "fruit" is a noncount noun (normally). Although we can say "Apples are fruit," we cannot correspondingly say "Dogs are animal."
Sentence (2), "My favorite animal is a dog," is OK if you are talking about a particular dog. Compare: "My favorite animal is Spot." The most proper sentence of the three, and probably the one that is the least likely to be used by native speakers, is (3), in which "the dog" is used in a toto-generic sense.