Combustible compounds react with oxygen to form lower energy oxidized compounds. Carbon is oxidized to carbon dioxide. A fully oxidized compound can’t be further oxidized under normal conditions.

Water is the most oxidized form of hydrogen. It can’t be further oxidized under normal conditions, hence why it’s not combustible.

Methane is the most reduced for of carbon, so it really wants to be oxidized. Carbon monoxide is only partially oxidized, so it’s still flammable.