The cycle Is a bit longer. Keep your eye on the carbon atom. Something like:
CO2 -> (C6H10O5)n -> CH4 -> CO2
The whole cycle takes about half a dozen years from atmospheric C02 back to atmospheric C02.
There is no "my theory" here that needs correcting. It's a matter of your "perspective". A matter of taking a few steps back, away from the details of chemical processes so you can see the whole elephant. Keeping your eye on the carbon atom can help with that if you insist on keeping zoom mode on.
Look at 100 years. Imagine a stable size Hurd of cows and a stable emissions natural gas leak, both producing methane.
Imagine measure both atmospheric CH4 and CO2 at 10 years in and 100 years in.
The CH4 levels will be equal at 10 and 100 years, the CO2 levels won't be. The rise in CO2 between year 10 and year 100 will be 100% attributable to the gas leak methane.
If you take a few steps back you will see it all starts to make sense, and if you are anyway like me, you will start feeling silly for not having grasped it before. It's easy to get blinded by the details, especially when powerful narrative has compelled you to do exactly that.
This form of thought probably has a name. One place that it has been demonstrated to me is from Isreali Zionists who tell North Americans to turn their attention to their Native Americans before pointing fingers at their treatment of Palestinians. As if colonialism in North America is any different than colonialism in the middle east. As if pipe line methane is different than that produced by the herds of cows that are not required for nourishment by most humans. It brings a picture of putting lipstick of a bovine to me.
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