Amoebas are often not symmetrical, although they could be if they wanted (and technically are Protista rather than animals).
Snails in general are not symmetrical internally or externally although their ancestors were.
Oysters are typically asymetrical.
Some owls aren’t strictly symmetrical because one ear is higher than the other.
The narwhal’s tusk is a left incisor which can grow up to 10 feet in length and forms a left-handed helix so they aren’t strictly symmetrical either.
Technically, people aren’t symmetrical because of handedness, and because the left human lung is smaller than the right to make room for the asymmetrical heart.
However, because of the mechanism of cell division symmetry is the most likely result in an animal. In addition, asymmetry is an indication of illness, injury, or generally be less fit than symmetrical fellows.