"Tomcat" is male in German, not female: Der Kater.
"Wife" is female in German, not neutral: Die Ehefrau. "Weib" is old language and rude to use these days.
replies(3):
All diminutives in German are neuter, for whatever reason. You could do the same for “Der Knabe” (“boy”) → “Das Knäbchen” (“little boy”).
Curiously, saying “Die Mad” would be as uncommon – at least nowadays – as saying “Das Knäbchen”.
It’s just one instance of the more general principle that the gender of nouns with a common suffix are based on the suffix. E.g. all nouns ending in -keit or -ung are feminine regardless of whether they have any connection to the biological female sex.