I posit that it's not necessarily wrong to strangle a dog.
Well, at least you're being philosophically consistent. The challenge with that view relates to how we, as a tribal, social species, likes to build relationships based on virtue signals, trust, contractual agreements, shared value of wellbeing, etc.
To be okay with causing a conscious being pain (this is something which can be measured in the brain, along with the reactions of the living thing being hurt, so maybe "harm" wasn't the best word) creates an ethical challenge. We describe sociopaths as people who don't have a "normal" functioning of empathy, compassion, mirror neuron use, etc, etc. Sociopaths don't care about hurting animals (or humans, for that matter). They are not trusted by most in society because of our shared value in increasing wellbeing (i.e. not causing pain when it can be avoided).
At this point we're probably getting to the "is / ought" problem. From my perspective, you're arguing for an evolutionary stable society as being "ideal" for us (and life in general). I can't really disagree with that and I love this video on the topic:
At the same time, we can control our environment. If we want to decrease suffering for conscious beings, we can. Should we? Should we limit that to just humans? Is painfully killing a dog wrong only because another human might claim "ownership" of that dog?
I'd love to do a Google Hangout or something to dive into these conversations more. I so enjoy them. :)