Earlier quoted context omitted.
Of course not. Unless you’re raising a deer herd, and claiming ownership over them, in which case sure.
When you put it that way it kind of sounds like managing the animal conversion of biomass into methane isn't the actual goal then.
Suppose you set up a polluting machine that solely emitted carbon, perhaps for art. That goal may be reasonable, but by engaging in it you’re hurting others. A carbon tax makes them whole (by either paying for carbon capture or by direct compensation) and disincentives you from doing it in the first place. If instead it was a naturally occurring polluting machine (a herd of deer, say) then we’d either want to remove it or do something to counteract it, and that cost is paid by everyone. In this case, we’d probably choose to plant trees, rather than killing the deer. (Although the deer population in North America is out of control, so perhaps killing them might be the right choice.)