I wonder if this double standard exists because of maternal roles placed on women.
Many people see pet's as surrogate children, or another version of children. People place high standards on mothers. Perhaps women with pets are seen as mothers, and what kind of mother abandons her child for a man?
Whiles with men, it's just seen as a hobby or weird indulgence until they get their own mommy, via a wife, where then they have actual children.