I don’t support the killing of animals. You are twisting what I said.
Our first obligation is to help other humans.
And you are not helping other humans by seeking to control what they do with their animals. Which are their property, not yours. If they bring an animal on your property or it annoys you, speak up. That's your right. But don't seek to tell other people what to do with their property.
That's where you're buying into the PETA line - assuming that you have the right to control others' property. That is a fundamentally anti-conservative position.