I think I've read somewhere that part of the reason Mr. Spiegelman drew people of jewish background as mice lay in the fact that Nazi propaganda posters often depicted jews as rats and mice in order to portray them as vermin and a social plague. I haven't run into any of this artwork yet, so I can't say for sure, but it sounds legit.
Also, I'm guessing there must have been a strong technical motivation for doing so. In order to illustrate his story, Art Spiegelman must have had to draw scores of real-life people he had never seen so much as a picture of. So in addition to the message it sent out, to draw people as faceless armies of mice and cats would have been an excellent solution to the technical limitations he had to face.