No, you, like a lot of people, read things like this all wrong.
All living beings sustain their lives at the cost of other living beings. They don't necessarily kill other beings, but they survive by eating/absorbing other being's remnants. So, yes, I eat meat and plants, and I don't disapprove of killing animals and plants for food - even dogs - even humans, if it ever came to that.
The point of all this isn't whether you kill or approve of killing. The point of this is WHY you kill. If you kill for food, that's fine with me. If you kill for self-defense, that's fine with me. But, if you kill for your convenience, or worse yet, for fun, that's not fine with me.
I believe most all of the supporters of killing soi dogs do so for convenience, not for self-defense (although that's what many suggest) and not for food.