That is not an accurate assessment of AGW. The current thinking basically balances an increase in particulate emissions which over the short term reduce global temperature average with greenhouse gasses which increase global temperature (plus a host of other factors). The fact that CO2 is extremely stable means than it accumulates in the atmosphere so its effects accumulate over time. Several other greenhouse gasses are modeled including water and methane, but their long term impact is reduced with time.
Now the long term stability of CO2 vs. methane is based on simple chemistry, and water rains. As to why CO2 would increase the greenhouse effect see: http://en.wikipedia.org/wiki/Absorption_spectrum and its overall concentration in the atmosphere.
PS: Looking back in history the accumulation effect of CO2 works in reverse so other man made impacts could have easily dominated it.
AGW is the theory of Anthropogenic Global Warming. Anthropogenic means "caused by humans". What you described is basic radiation transfer and mass balance.
Well if you accept the physics of increasing CO2 in the air. Then you need to look at the chemistry of burning the gigantic quantities of mostly solid carbon in Coal C + O2 in the air => an even larger quantity of CO2 by volume in the air. Some basic math on the mass of Carbon released from Coal + Hydrocarbons (which mostly end up as CO2 and H20 after complete combustion) you find that tracks with the increase of CO2 in the air.
Like most complex scientific theories there are several steps of logic involved. And while a few groups agree on which specific steps break the chain a slightly larger but still small group of people can agree that it's broken.
Now the long term stability of CO2 vs. methane is based on simple chemistry, and water rains. As to why CO2 would increase the greenhouse effect see: http://en.wikipedia.org/wiki/Absorption_spectrum and its overall concentration in the atmosphere.
PS: Looking back in history the accumulation effect of CO2 works in reverse so other man made impacts could have easily dominated it.