I used to advocate for the same thing, but someone on Reddit helped clear up why we shouldn't.
This isn't a perfect world. People have biases. Someone has to draw the line of what should be killed and what shouldn't be killed. There will always be people trying to redraw that line elsewhere, and many arguments against where the line is no matter where it is. There will never be a best-case scenario where everyone agrees on who's getting killed because of what.
Another excuse against killing them is a practical answer, rather than a political answer. People argue for the practicality of killing them all because they waste resources. I'll argue that the loss of resources is paying people to deal with them. Their existence creates jobs in the caretaking market, and lobbying for more laws dictating their care would possibly make more jobs in that market, while killing them all would put many people out of a job.
I hope these two, non-emotionally charged answers might help people make a better decision on where they stand on this issue.
