You don't get it, do you?

The "genocide" that you describe is happening constantly. None of the chicken we have today will be alive in a couple months. We kill them to eat them.

If we cease to "use" them, we just keep that "genocide" going for a year, but we just stop breeding new ones. The result is no more animals after a few months/years. And you didn't kill any more than you would have anyways.

If you have a sink that is half full because the inflowing water and the outflowing water are in quilibrium, you drain it by turning off the tap (breeding).