Geologic reconstruction of past climate (see figure below) shows a sharp DROP of 10C during the late Ordovician of the Paleozoic (~488 to 444 million years ago) while atmospheric CO levels INCREASED from ~4100 ppm to 4500 ppm. This climate change reflected the onset of one of the coldest Ice Eras in Earth's climate history and demonstrates conclusively that there is no causative relationship between atmospheric CO and global average temperature.
Fallacy: false equivalence