As similarly suggested by Wally Hastings (1998), in his online article about Maus, By distancing the reader from the experience, the talking animals enable us to bear the horror implicit in the Holocaust memory."

Art Spiegelman made use of different animals to depict the different nationalities in the story because he perhaps found that the use of animals is the easiest and simplest way to characterize the people in the Holocaust. For instance, he made use of the mice to represent the Jews. The Jews, similar to mice, can become weak and vulnerable victims. The Germans, who without heart had massacred the Jews during the Holocaust, was represented by Spiegelman as the cats; for the cats' malevolence characteristic, in which after capturing a mouse plays with it first then brutally killing...

Characterizing the different nationalities as animals, where some were represented by Spiegelman as endearing creatures while the others were offensively represented by unpleasant animals, may be Spiegelman's way of showing to the different nationalities in the Holocaust, and making them feel as well, how stupid and shameful it is to classify humans based on their race.
Bibliography

Hastings, Wally. Art Spiegelman's Maus. 1998. http://www.northern.edu/hastingw/maus.htm