Correlation is not causation - though sometimes it's the opposite.

What first opened my eyes (I admit to being a AGW believer in the late 90′s) was the CO2-temperature graphs. They’;re beloved by the AGW crowd because they show a relationship (correlation) between the two, a very strong one. They use this to argue causation. Turns out, there’s a huge problem with that.
The CO2-temperature graphs show a close tracking for the last 400,000 years (ice core data). If, as was done, the two are separated by height on the graph, only the relationship is evident. (and that, I suspect, is why they present it in that format)

The real eye-opener is when you overlay the two lines. Then, you clearly see what isn’t easy to see on the most commonly used charts – a time lag. It varies from 2 to 10 centuries (it trends toward the lower limit in warming periods, the longer in cooling)

It’s the time lag that’s the key. What it boils down to is the cause must come before the effect.
Short version: it’s absolutely clear in both the Greenland and Antarctic ice cores that there is a relationship between CO2 and temperature. Temperature goes up, *then* CO2 does the same. Temperature goes down, so does CO2. The two, when graphed, do track each other. But it’s temperature, not CO2, that’s the leader; CO2 follows temperature (by several hundred years) not the other way around.

This is most clearly evident at both the start and end of the most recent glacial era. At the end of the Eemian interglacial, temperature and CO2 diverged massively; CO2 continued to rise for several hundred years after the drop in temperature. Likewise, at the end of the last glacial era, temperatures rose several hundred years before CO2 began to rise. This is also true (though based on antarctic ice cores only) of the prior four glacial eras, so five glacial eras in all. It’s evident through the entire timeline not just at the glacial era interfaces, but it’s most obvious there.

So, unless we want to assume violations of the law of cause and effect (or time-traveling CO2) then it’s abundantly clear that temperature drives CO2 levels, and not the other way around. This makes sense, because while it’s difficult to beleive that a gas that’s a tiny fraction of earth’s atmosphere (four hundredths of one percent) could have a major impact on temperature, it’s very easy to see how temperature, through its effects on both geochemical and organic processes, could have an effect on trace gas levels. (and also, why there’s a time lag in this effect).

Now, we get to the Eemian interglacial era (the last interglacial warm period prior to the one in which we live). CO2 levels then were lower than today, and also lower than our per-industrial levels, yet the climate then was both hotter and wetter, worldwide. This is seen clearly from the fossil record in many location on earth; hippopotamus fossils on the Thames in the UK, iguanas in Greenland, tropical shells in presently-temperate areas… and most glaring of all, raised coral islands worldwide. (surface level coral reefs in the Eemian, when sea levels were about 17 feet higher.) It’s true that in some cases raised coral islands are caused by geologic uplift, but that’s not the case with most. Yet, all over the globe, even in areas where it’s currently too cold for coral, we see raised coral islands of approximately the same height, all dating from the Eemian.

The AGW claim is twofold. First, they denied (ahha, deniers!) that the Eemian was warmer than the present (Much as they currently still do regarding Holocene warm periods, such as the Medieval Warm Period, that was warmer than today) . Then, they adapted, and now the current commonplace AGW explanation for the Eemian is that this warmth (that they denied) was due to solar forcing, not CO2. If that were true, it would, amongst other things, negate the cause and effect they claim from the close tracking of CO2 and temperature.
Some of the current warmist claims are that the Eemian was only warmer in non-polar regions, and was colder at the poles, and that’s why polar bears didn’t go extinct, and thus global temp averages weren’t warmer than today. Unfortunately for them, this doesn’t pass the snicker test; the ice cores, especially in Greenland, show this isn’t the case, and it also ignores the higher sea level. Even if every bit of Greenland ice (the only significant ice volume in the northern hemisphere) melted, it’d raise sea levels by about six feet. The sea ice on the arctic ocean is meaningless for sea level changes, because it could all melt and not raise sea levels at all (it’s floating, of course).
So, that leaves Antarctic ice as the source of the majority of the Eemian high sea levels (the water had to come from somewhere, and that’s the only source large enough). So, taken to a logical conclusion, the current AGW claims for the Eemian can be summed up as “the ice melted because it got colder”. They can’t claim sublimation; precipitation was higher then, too.

But, that makes just as much sense as time-traveling CO2.