Here's why:
* "Either" is a conjunction. It's used to connect two or more alternatives, but it doesn't have its own meaning or act as a noun.
* The subject must be a noun or pronoun. In this sentence, the subjects are "dog" and "cat," each representing a potential agent of the action.
Corrected Sentence:
* Either the dog or the cat scared the mouse.
In this corrected sentence, "the dog" and "the cat" are the subjects, each connected by the conjunction "or."