@pschwede Well we dont have to, not exactly, because of #3... think about it like this...

So if we accept there is strong correlation between temperature and CO2 that means either changes in temperature effect the world in a way that causes CO2 levels to change. Or CO2 levels cause the temperature to change, or perhaps even both, where changing one always changes the other.

Whichever of these it is all we need to do is ask ourselves a few simple questions:

How much has the CO2 changed in recent years?

How much CO2 have humans put into the atmosphere in that time?

Is the portion of CO2 increased in the atmosphere mostly accounted for by human processes such as pollution or is the volume much greater than the known human contribution?

Well earlier you said you conceded point 3 which was that humans contributed the bulk of the change int he CO2. So if you recognize this fact, then the fact that we can observe the temperature changing exactly the same as the correlation shown historically, we can therefore conclude that a change in CO2 is the causative agent resulting in the change in temperature. After all if it was the other way around then we wouldnt see any change in temperature from all the CO2 we are dumping, yet the correlation continues to track just as perfectly as it did historically.