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.
Therefore, when we breathe out, all the carbon dioxide we exhale has already been accounted for. By performing cellular respiration, 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!