Why should the amount of carbon in the atmosphere stay the same?

Photosynthesis and respiration should balance each other out.

Cellular respiration and photosynthesis are both dependent on each other, thus creating a cycle. Respiration creates carbon from oxygen, while photosynthesis takes that carbon created and reuses it to make oxygen. If they are creating/using carbon at the exact same rate, everything should stay the same. I think that's the answer you were looking for, anyways. Hope I helped :)