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All IPCC definitions taken from Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Annex I, Glossary, pp. 941-954. Cambridge University Press.
By breathing out, we are simply returning to the air the same CO2 that was there to begin with.
The very first time you learned about carbon dioxide was probably in grade school: We breathe in oxygen and breathe out carbon dioxide. Any eight-year-old can rattle off this fact.
It should come as no surprise that, when confronted with the challenge of reducing our carbon emissions from the burning of fossil fuels, some people angrily proclaim, "Why should we bother? Even breathing out creates carbon emissions!"
This statement fails to take into account the other half of the carbon cycle. As you also learned in grade school, plants are the opposite to animals in this respect: Through photosynthesis, they take in carbon dioxide and release oxygen, in a chemical equation opposite to the one above. (They also perform some respiration, because they need to eat as well, but it is outweighed by the photosynthesis.) The carbon they collect from the CO2 in the air forms their tissues - roots, stems, leaves, and fruit.
These tissues form the base of the food chain, as they are eaten by animals, which are eaten by other animals, and so on. As humans, we are part of this food chain. All the carbon in our body comes either directly or indirectly from plants, which took it out of the air only recently.
This new animation published by Dr. Patrick T. Brown (Carnegie Institution for Science, Stanford University) in September 2018 explains the process:
Therefore, when we breathe out, all the carbon dioxide we exhale has already been accounted for. We are simply returning to the air the same carbon that was there to begin with. Remember, it's a carbon cycle, not a straight line - and a good thing, too!
Update information: This rebuttal was updated on September 12, 2018 to swap the graphic showing a - to some - "odd looking cow" with the new video we happened to notice on Twitter. Thanks to Patrick T. Brown for making it available on YouTube!