A Talking Animal (or at least someone who looks like one) is constantly mistaken for another species as a Running Gag. Often, it can be their Berserk Button, particularly if they consider it a Fantastic Slur. This trope often leads to Insistent Terminology or Have I Mentioned I Am a Dwarf Today?.
The Trope Namer is Cow and Chicken spinoff I Am Weasel. Not to be confused with I Am Not Shazam. Compare with Son of an Ape, a variant by which comparing humans to other primates is considered insulting. Contrast with the inversion, Ass in a Lion Skin, for when an animal wants to be taken for another species.
See Mistaken Ethnicity and Mistaken Nationality when it is happening with humans for ethnicities or nationalities respectively, or Accidental Misnaming when dealing with proper names, or I Am Not Spock when dealing with actors and their characters. See also A Dog Named "Cat", where an animal is named after a species it's clearly not. If it's the viewers that are confusing a character's species, then that's Viewer Species Confusion.