New Hampshire's House recently passed HB1410. This law redefines domestic violence to include animal cruelty. Cruelty in this case is defined as "acts or omissions injurious or detrimental to the health, safety or welfare of any animal, including the abandoning of any animal without proper provision for its care, sustenance, protection or shelter." The text of HB1410 is here. The legal definition of animal cruelty is here.
This can result in any person that breaks up with their domestic partner and moves out of the house without making arrangements for the goldfish to be taken care of being slapped with a domestic violence restraining order, even if there is no evidence that the person in question has committed any violent act. This, in turn, will result in the person in question becoming a "prohibited person" for the ownership or possession of firearms under Federal law.
Slippery slope is not a fallacious argument.