Why do they call a mouse on the computer a mouse not a rat?

Because the Word "mouse" has friendly and nice connotations. Mice are cute and fuzzy. Mickey Mouse, Jerry Mouse, Danger Mouse, people like mice.

The Word "rat" has very negative connotations. If someone is sleazy and immoral, they are a "dirty rat," or "rat fink"... rats are associated with black plague, people generally don't like rats.