I'm afraid you are making a very common error; assuming correlation means causality, when correlation is only a necessary condition, but not a sufficient one.
You have also assumed, as did Hansen and others early on, that by knowing how much CO2 we dump into the atmosphere, and we do know it, that simple arithmetic would give us the amount of observed CO2 increase that is due to mans emission of CO2.
That, of course, requires a closed system like a Mason jar filled with whiskey and water. We pour in 50 ml of Jack Daniels and observe that the total volume of liquid in the jar is 500 ml. We conclude that the Jar contains 10% by volume of Jack Daniels for which we are responsible. Any other Jack Daniels that's there is not our doing.
But now assume the jar is not a closed system, and that not only do we add Jack Daniels but there is a pipe dumping Jack Daniels into the jar at an unkown rate. Then further assume there is still another pipe removing Jack Daniels at another unknown rate. Assume these extra pipes are connected directly to the Brewery, so that, compared to our one-fifth supply of Jack Daniels, their source of supply is orders of magnitude greater. And there are two more pipes, one dumping water into the jar at an unknown rate and another removing it at an unknown rate but at just the right rates to keep the total volume in the jar at 500ml.
The best we can due now is to sample the liquid in the jar and determine how much Jack Daniels is there at any moment. But we have no idea what fraction of the Jack Daniels that's there at that moment is due to what we put in! And to make matters worse, If we check the concentration of Jack Daniels some while later it will have changed. In this relatively simple dynamic system we can't make much sense of our Jack Daniels measurement without knowing the rates for addition and subtraction of Jack Daniels and elapsed time. But if we could make enough measurements over a long enough time we could eventually figure out exactly how the Jack Daniels concentration would change with time, assuming all the rates of addition and subtraction of substances to the jar were constant and did not change while we were trying to make our measurements.
I have described is extremely simple system, however, compared to the chaos of the Earth's atmosphere and its dynamically changing gas concentrations. One can not make simple calculations to arrive at what fraction of atmospheric CO2 is due to man without making assumptions about the relative size of the temperature dependent rate constants affecting the various dynamic CO2 equilibria. And of course we have to know what the equilibria reactions are to start with. I question the validity of the assumptions being made given our current state of knowledge.
I'd like to suggest that you attempt to read your chart a little more carefully, paying attention to the lining up of points on the time axis with those on the corresponding CO2 ppm and giga tons of carbon axes, respectively. What does the chart say to you about the timing for anthro CO2 emission relative to total atmospheric CO2.
You see, FC, for a long while most scientists just assumed that the climate science that was receiving so much attention was being done correctly. The only ones with serious questions were the experts who from early on had concerns about the data's interpretation, and there was a paucity of good data until recently. But the matter had so quickly become politicized that these expert's protestations were not being heard. Now, finally we have enough highly competent experts, such as Salby, getting involved that the questions are being paid more attention and defects in the early work are at last getting the exposure they deserved all along. It is finally being recognized that the experts raising the questions have nothing to do with the Koch Brothers, the fossil fuel industry, or the Republican Caucus, but are disinterested scientists. Science will, I assure you, win out in the end, but it may take a while.