A green parrot in front of a green plant, for instance, probably won't cut it. Some pets are just harder to photograph than others. Dark-colored pets can be a challenge. All-white animals can also be tough. Medium to light shades are often the easiest to capture nicely on film, thus the volume of great shots of pets such as Golden Retrievers.
Small animals are usually harder to photograph than larger pets.
In getting close to shoot, say, a mouse, focus becomes critical and tougher to control. Your camera equipment can be part of the solution, or part of the problem. When and where you are shooting also can have a huge impact on your pictures. Indoors is rarely optimal, unless you have a good flash system and know how to use it. Shooting in a dimly-lit room without a flash is usually a complete waste of time and film.