I think a key difference is when society considers it a crime. Animal cruelty or neglect is generally a crime. Setting your house on fire can be prosecuted as arson. The issue of whether it is your own property can be immaterial in such considerations. Each person has to make their own determination over which scenarios they feel compelled to intervene appropriately.
Fair point, especially if the arson is malicious and hurts a third party.
But, I have witnessed examples of both (deliberately setting a building afire & animal cruelty) that in no way would justify some third-party twit intruding on the proceedings.
Building Fire:
1. If the home is not owned outright & mortgage-free by the fire-starter, the bank that holds the mortgage & title is the true owner. They are injured by the destruction of their property. Not applicable to property owned outright like one would presume a dog would be.
2. If the home is near others, setting it on fire is a risk to those others who may burn down, too. Not applicable as the poor dog's death is not going to injure neighbors.
3. If the fire-starter tries to collect on an insurance policy, the insurer is injured. Not applicable, unless dog is insured and the owner tries to collect.
FTR, I have family in rural parts who have deliberately destroyed buildings(1) and deliberately burned property. None of the three exceptions above applied, so they went about their business, unmolested.
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"Animal Cruelty" laws are a recent innovation by those who wish to insulate themselves from the reality of human/animal and animal/animal interaction. Like the chickens vs doggie example, as long as it happens out of sight, folks are more than happy to ignorantly feast on the proceeds of cruelty to animals.
Have the jokers who wrote those laws ever been to a slaughterhouse? Or even a farm? Have they ever eaten meat not sourced from the grocery store? More cruelty and death to fill a supertanker in one meat-packing plant. Heck, do they even know what happens to Rex when he is taken to the vet to be neutered?
Bah, it is all eyewash. Every bit of it. It makes us uncomfortable so we banish it from our sight and punish those so gauche as to remind us.
Again, family in rural parts provided opportunities to do all sort of cruel things to animals in the normal course of running a farm. So much that if there were some way to quantify cruelty, one poor dog dying of heat stroke in suburbia would be a drop in the bucket.
Besides, private property either means something or it doesn't. "You can do with as you will with your property unless I think you oughtn't, even if it harms no other person" is not a formulation congruent with liberty or respect for property rights. This is not to say that use of moral suasion & social pressure are not valid. I think both ought to be used early & often.
(1) Why? In one case, property taxes. He wasn't using the building enough to justify the property taxes he paid on it. So, it got torched and off the tax rolls. "Burning an outbuilding seems extreme. Why not just tear it down with a front-end loader?" OK, then what do you do with the great big pile of lumber? Gonna get burnt anyway.