I believe it's based on the fact that the combustion of CH4 produces somewhat less CO2 per evolved BTU than the combustion of other hydrocarbons. ( 117,00 lbs/billion BTU versus 164,000 lbs for "oil" : NaturalGas.org )
This leads to the doctrine that it is a "cleaner alternative", and hence an "alternative fuel".
Yes I agree that combustion generates somewhat less CO2. Natural gas is in short supply however. Severe restrictions on oil extraction are also restrictions on natural gas exploration. Even in places where natural gas is extracted without oil extraction, the left tries to stop natural gas exploration.
My point is that natural gas should be used for its most efficient usages (heating) rather than promoted as an alternative to oil and coal. If natural gas was abundant, inexpensive, and easy to extract, oil and coal substitution would make sense. The left hates natural gas almost as much as oil and coal. If oil and coal are abandoned, the left will find plenty of reasons to dislike natural gas.