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.

The goal is to fix the current phenomenon where human activity dumps enough co2 (and other greenhouse gases like methane) into the atmosphere to significantly alter the global climate and cause massive problems.

By the way, deer are not a meaningful contributor to atmospheric greenhouse gas levels.

If you’re raising the deer, then you’re responsible for the externalities produced by your economic pursuit. If you’re not raising the deer, then they’re the responsibility of humankind as a whole, who is already paying for those externalities (by having to suffer from climate change). The point of a carbon (or methane) tax is to ensure that you pay for your externalities, both to disincentivize you from having them and to repay everyone else for the cost that they’ve been dealt by you.

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.)