Here’s the density of temperature changes over centuries. I used these data and calculate the average change in temperature per century.
Last century’s temperature increase of 0.8 degrees C was an outlier (but not an extreme outlier). About 95% of temperature changes were slower than last century’s temperature change. If the climate models are correct and the world sees a 2.5 degree increase, this would be an extreme outlier. Only about 1 in a three or four hundred centuries sees that dramatic of temperature changes.
This, of course, doesn’t guarantee catastrophe, but it suggests we should at least insure ourselves against the possibility of catastrophe.