One possibility is that what the analysis has found is a correlation between temperature and short-term variations in atmospheric CO2. However, this isn’t counterintuitive, because it is well understood and is largely a result of seasonal variations in vegetation. What the paper seems to be implying is that the long-term rise in atmospheric CO2, that started in the mid-1800s, has been caused by the increasing temperatures, and – hence – that this rise in atmospheric CO2 has not driven the increase in global temperatures.

This is not counterintuitive, it is simply wrong. The rise in atmospheric CO2 is almost entirely due to human emissions of CO2 into the atmosphere. Similarly, it is the increase in atmospheric CO2 that is driving global warming. Both of these are results for which there is a huge amount of supporting evidence and which are unlikely to be overthrown by a statistical method for determining causality.

The error made by Koutsoyiannis et al (hereafter K22b, K22a referring to doi:10.1098/rspa.2021.0835 and K22 referring to both papers) is not too difficult to identify as it is a mistake that has been made before to argue that the rise in atmospheric CO2 is a natural phenomenon, for example Murry Salby and Humlum et al (see comment papers by Richardson and Masters & Benestad). In this case, it provides a salutary lesson in the dangers of strictly statistical conceptions of causality - if we are not extremely cautious in interpreting the results, we can easily be misled.

The method of K22 shares a feature with Grainger causality in that it determines the direction of causality according to whether future values of one time-series signal are best explained by past values of a second time-series signal or vice versa (or "Hen or Egg" - HOE, see figure 1 of K22a). The approach taken by K22 is different, but this is still a key feature of the method. A limitation of this approach is that no causal association can be inferred between two linearly increasing or decreasing signals:

K22a contains an interesting discussion of philosophical views on causality, but I think it missed the opportunity of highlighting the mismatch between common sense and statistical conceptions of causality.

"lee" is not a high school drop out. You can tell that he is a bit of a professional student.