The short answer is that when we breathe in air, there's more than oxygen in it. About 20% is oxygen, about 80% is nitrogen, and less than one percent is carbon dioxide.

But we breathe out more carbon dioxide than we breathe in. Our cells all need oxygen to stay alive. They use it in the process of breaking down sugar to release the energy we need. Our lungs bring in air, and the oxygen flows from the air in our lungs into our blood. Then the oxygen flows from the blood into the cells that need it. The cells basically "use up" the oxygen and produce carbon dioxide (CO₂). This CO₂ flows into the blood, is carried back to the lungs, and breathed out.

The molecules that make up the CO₂ and oxygen don't disappear, they just get rearranged.

Sugar (C₆H₁₂O₆) and 6 oxygen (O₂) go into the process and 6 carbon dioxide (CO₂) and 6 water (H₂O) come out.

Plants use the sun's energy to make sugar out of water and CO₂. What do they "breathe out?"