Starting with the premise of human activity...
The big challenge here is not to prove that the globe is warming or cooling. There are an amazing number of things that effect the global climate, and it is going to keep changing. I think most of the people on both sides of this issue agree that the climate is different from decade to decade.
The question is around man's contribution to, and possible control of, the changes. Sometimes we are ignorant of what we cause, and sometimes we are arrogant enough to think it all revolves around us. And somewhere in there is the truth.
Those who are asking that man’s production of CO2 be reduced start with the premise that man is the primary driver in the changes in global CO2 levels. There is the secondary premise that CO2 levels are the primary driver of global temperature change. Given all the variables in the second, I have so far focused on the first.
If man is the primary driver of global CO2 levels, then there should be a reasonable correlation between the changes in man’s production of CO2 (from fossil fuels) and the annual change in the global CO2 levels. Given such a correlation, it seems clear that to then reduce the levels of human CO2 production could slow, or even reverse, the increases in global levels.
Unfortunately, the current data does not show a good correlation between the annual changes in CO2 levels and the annual rate of fossil fuel consumption. The global levels, measured in Antarctica for 20 years, do show an always increasing trend. However, the rate of increase each year varies wildly. You can find the data here:
http://cdiac.ornl.gov/trends/co2/jubany.html
And a summary of global carbon output here:
http://cdiac.ornl.gov/trends/emis/glo.html
You can build a statistical analysis to look for the correlation between the rate of annual increase in global CO2 (I use the December numbers, but the annual averages work as well) and the rate of annual increase in human CO2 production. My calculations on the data show no meaningful correlation at all, which makes it difficult to believe that they are causally related. Here is a small sample, during times of fluctuation in human activity:
Year Human CO2 Atmosphere CO2
1999-2000 up 2.46% up 0.24%
2000-2001 up 2.40% up 0.64%
2001-2002 up 0.93% up 0.56%
2002-2003 up 5.52% up 0.42%
2003-2004 up 4.95% up 0.62%
If the human production of CO2 is driving the global CO2 levels, then I am sure there is a model that explains why they are not changing in ways that are more closely related.