As I read the chart, CO2 tracks temperature. There is a very pronounced lag between periods of increased temp., and increased CO2 which would say global warming increases CO2, not the other way around.
"...which would say global warming increases CO2, not the other way around..."
Which makes enormous sense if you think about it. Life thrives on warm temperatures. A warmer planet produces more life, and the balance of plants to animals would likely shift since animals on average reproduce more rapidly than plants.
More animals means more CO2.
The theory behind using tree rings to infer temperature changes is based on the fact that trees grow better when sunlight is brightest which likely occurs on warmer days; trees also grow faster when they have an abundance of carbon dioxide which suggests a certain synergism once the two become coexistent.