With no responsibility comes no rights
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It’s not a perfect saying, I realize. Babies have no responsibilities and still have rights (to life), for instance. But they do not have a right to vote or drive. They have human rights because they are human.
Similarly, we don’t have the right to indiscriminately destroy the created order for fun and profit. Why? Because it doesn’t belong to us. We are stewards of God’s garden. But we still have dominion and animals are not our equals, as The Onion points out. Animals do not enjoy human rights. Why? Because they are animals. Creatures enjoy a certain respect due them because they are the creatures of God. Ancient Israelites even had strictures against unnecessarily harming trees in the heat of battle:
When you besiege a city for a long time, making war against it in order to take it, you shall not destroy its trees by wielding an axe against them; for you may eat of them, but you shall not cut them down. Are the trees in the field men that they should be besieged by you? (Deuteronomy 20:19)
But ancient Israelites were not tree huggers. They emphatically grasped that there is an ontological difference between humans and the rest of creation and instinctively avoided the folly of current “animal rights” types who think the solution to our abuse of creation is to erase the distinction between humans and the rest of the created order.