But the thing is nobody is calling cow farts "natural gas"; they call them "methane". Even the wikipedia page for "natural gas" refers solely to the fossil fuel we get out of the ground:

Natural gas (also called fossil gas, methane gas or simply gas) is a naturally occurring mixture of gaseous hydrocarbons consisting primarily of methane in addition to various smaller amounts of other higher alkanes. Low levels of trace gases like carbon dioxide, nitrogen, hydrogen sulfide, and helium are also usually present.[1]

Natural gas is a fossil fuel and non-renewable resource that is formed when layers of organic matter (primarily marine microorganisms)[4] decompose under anaerobic conditions and are subjected to intense heat and pressure underground over millions of years.[5] The energy that the decayed organisms originally obtained from the sun via photosynthesis is stored as chemical energy within the molecules of methane and other hydrocarbons.[6]

I think the key distinction is that "natural gas", as a term, only actually refers to the fossil fuel. That is, "natural gas" != "methane".

The meme is about stopping saying "natural gas" — i.e., the fossil fuel, not other non-fossil sources of methane — and instead calling it "fossil methane". Given we already call cow farts methane and landfill emissions methane, calling the fossil fuel form of methane "fossil methane" seems fitting to me. That way we have overall methane, then we can specify source by saying "fossil methane" or "landfill methane" or "agricultural methane" and so forth.