Where are you getting the carbon from?
For a "carbon neutral" process, you would have to use atmospheric carbon dioxide, which is at a concentration of 0.04 percent.
Mass of CO2 is 1.977 kg/m3 , so there are ~ 0.0007908 kg/m3 of CO2 in normal air
In that CO2, carbon represents 1/5th of the mass,
So that's 0.00015815 kg carbon / m3 of air.
Methanol is the simplest hydrocarbon that is liquid, Its molecular mass is 4+12+16=32 , of which 12 is Carbon, so 3/8s carbon. So you can make 0.0004217 kg of methanol per m3 of air.
~3 kg's of Methanol make a gallon, so if you extract the CO2 from 7114 m3 of air you can make 1 gallon of methanol (and a bunch of oxygen). That's 9 tons of air you have to process somehow, per gallon.
In the past , the only cost efficient way to process that much air has been self replicating carbon dioxide processing systems. Otherwise known as trees and plants.