For most of the ways methane breaks down, it gets converted to CO2 anyway[1]. So it's better to break it down to CO2 immediately to avoid the stronger greenhouse effect of methane.

[1] https://en.wikipedia.org/wiki/Atmospheric_methane#Natural_si...

Your link suggests your assertion "For most of the ways methane breaks down, it gets converted to CO2 anyway" is just plain incorrect. In the atmosphere, methane becomes -CH3 (- used for dot because I don't know how to do that), the free radical eventually forms formaldehyde. Methanotropic soil bacteria can break down methane to CO2, but there is nothing to support your assertion that most of the ways methane breaks down [make] CO2.

The page at that link says:

« The most effective sink of atmospheric methane is the hydroxyl radical in the troposphere, or the lowest portion of Earth’s atmosphere. As methane rises into the air, it reacts with the hydroxyl radical to create water vapor and carbon dioxide. »

So if the page is right, possibly not "most of the ways", but at least "most of the methane".

There are multiple reactions involved. The methane gets converted to formaldehyde, which gets converted into CO, which then gets converted into CO2.