Let's imagine I have a lab and I have three gas tanks that can store CO2. I've a really big tank I'll call the Deep Ocean tank. I've a smaller tank which I'll call the Shallow Ocean tank. And I've a yet smaller tank which I'll call the Atmosphere tank.
What I now do is stick a series of pumps between the tanks. So I've a pump system that sends CO2 from the Deep Ocean to the Shallow ocean tank. I've a pump system that sends CO2 from the Shallow Ocean tank to the Deep Ocean tank. I've a pump that sends CO2 from the Shallow Ocean tank to the Atmosphere tank. And finally, I've one that sends CO2 from the Atmosphere tank to the Shallow Ocean tank. I fill each tank with some CO2 and set the pump speeds to different rates. The pumps between the Shallow to Deep Ocean tanks are slow. The pumps between the Shallow Ocean and Atmosphere are fast. And I plug them all in and then I watch what happens ...
There's only a limited amount of CO2 in the entire system. As it starts off, it's a mess ... CO2 levels in each tank rise and fall as the pumps work away. But if I leave it, the whole system will settle into a steady-state condition where there are certain levels of CO2 in each tank that remain pretty constant based on the relative speeds of the pumps. If I decide to change the speed of a pump, then the whole system readjusts until eventually it settles down and I have new levels of CO2 in each tank.
What happens is that, due to Milankovich cycles (the eccentricity of the earth's orbit about the sun), the earth receives slightly less energy from the sun and so cools and then receives more energy from the sun and so warms. When the earth is warming, oceans begin to release more CO2. In other words, warming increases the pump speed between the Shallow Ocean and Atmosphere tanks. We start to see CO2 levels rising in the atmosphere. But this CO2 also has a warming effect. So the process is something like planet warms - pumps change speed - system begins to respond - CO2 levels in Atmosphere tank start to increase - increase in CO2 warms the planet - pumps change speed because of that temperature rise ... and so on. The CO2 level is affecting the pump speeds which is related to temperature, but the Shallow Ocean to Atmosphere and the Atmosphere to Shallow Ocean pumps aren't affected by the same amount. The CO2 increase lags behind the temperature rise because the temperature rise was initiated by the change in orbital position of the earth. The exact opposite process occurs when the earth cools, but now the level of CO2 in the Atmosphere tank is more associated with how fast the Atmosphere to Shallow Ocean pump runs. This is why if you look at the graph you see a rapid increase in temperature/CO2 but a slow decrease.
The point, however, is that all nature is doing is playing around with pump speeds between tanks with a certain amount of CO2 in them. The question is what happens when I go and add MORE CO2 into the Atmosphere tank. This is a completely different scenario to the one we just looked at. It's a whole new experiment. And the observations we made previously aren't applicable now!
What happens is that the levels in the Atmosphere tank increase because I've added more CO2. That CO2 starts to warm the planet, so it adjusts the pump rates between Shallow Ocean and Atmosphere and vice versa. It doesn't affect each pump equally. Now, if I left it alone, eventually the system would settle and I'd get some steady-state levels again. But before it settles, I add a bit more CO2 to the Atmosphere tank. Damn! Now I've affected the pump rates AGAIN. So I'd have to wait for it to settle. But sod that! I'll add some more CO2. And you can see now that what I'm doing is *completely* different to the situation we had before.
This is why there is a lag between temperature and CO2 towards the end of the graph. What we're doing is changing CO2 and watching how it affects the pump rates (temperature) rather than changing the pump rates (temperature) and watching how it affects CO2 levels! As I said ... different experiment!