We shot them, butchered them, and turned them into cat and dog food. That's how the pet food industry got its start.

Good example for your argument, maybe, but I doubt it's going to win you many converts.

It's a lot easier to stop horses breeding.

If automation ever gets to the point where a law guaranteed basic income is required, there's no reason that incentivized or mandatory sterilization can't be required as well, especially if made a prerequisite for said basic income.