The TED talk that is linked in other comments debunks this too. All the CO2 exhaled by humans is short-term carbon that was recently taken out of the atmosphere by a plant. All plants and animals are short-term carbon sinks. The damage is caused by burning fossil fuels.
I suppose there might be a few artificial ingredients that are made from petroleum feedstock, and thus human metabolism cause it's first release as CO2, but it's tiny compared to the sugars and fats we consume from plants and animals.
It has to be either in equilibrium, or in excess on the side of plants. If it's in excess on the side of humans, people would be dying out due to lack of food, which would then put it back into equilibrium. Deforestation isn't relevant to food because we don't eat trees.
