A common trope in fiction of the time was that of an aging married couple that does not divorce but that quietly… or even secretly… resents each other.

In contrast, pets are almost universally loved. The idea of living with a pet that you have a quiet resentment for is is humorously foreign and surprising.

Another comment in the thread is hinting at an obscure reference. If there is such a reference, I don’t get it either. The cultural touchstone of the resentful married couple is clearly part of the bit though.