Fuel companies sell fuel. They aren't burning it. The fuel companies' customers would be the ones responsible for the emissions.

They sell fuel having prepared it for burning, put it in tankers, and sent it to sites that pour it into the machines that burn it. Ergo they are responsible for its impacts, and should be taxed, regulated and penalised accordingly. The entire environmental impact should be on the producer and seller, and fully priced into their sales. Customers would then be incentivised to find a more economic, and less impactful fuel.

there are fuel companies because there are billion people in their cars, of course it's something to tackle as well, I don't own a car personally

But a pet is equivalent to 2 4x4 cars: https://en.wikipedia.org/wiki/Pet_food#cite_note-8 so it can't hurt to start with that, or with anything else that would reduce pollution basically, at any scale. The problem is the accumulation, if most people reduce their environmental footprint by a half, the effect is very significant, it's like twice less humans

Everything that people own has some carbon cost associated with is, so the mere presence of a carbon cost doesn't justify getting rid of it.

Why would you argue that pets specifically are something that people should give up? People have needs that go beyond food, water, and shelter (e.g. play, love, stimulation, etc.) that will have to be factored into any plan to reduce carbon emissions. It seems to me that pets are an excellent value in terms of degree to which they provide for their needs versus associated carbon cost.

Yes we have needs, but the planet has limits that we already hit, so we now should all have a moral duty to limit/filter our non-essential needs

The sources show how significant pets impact is (1/5th of the world meat+fish production, think about the processing, transport, and all intermediate materials required for this and the pollution that generates, and finally the ecosystem damages via outdoors and feral ones)

I see what you're saying, but I'm not sure that the needs that pets supply are non-essential. For many people they are a significant, if not primary, source of companionship and joy. I think we would need a plan for how to offset removing something so important.