We also over estimate the volume of the atmosphere -- it is very thin. If the Eaarth was a ball then the atmosphere is thinner than a coat of varnish.
Carbon dioxide from breathing is just recycling the oxygen that the plants have put out. It depends on the source of the carbon: "old" carbon that was underground for millions of years that get reintroduced to the air is NOT the same as carbon dioxide that comes from burning wood, for example. That is "new" carbon, or "short-cycled" carbon -- it is the "long-cycled" carbon that is increasing the carbon dioxide in a geological blink of an eye.
The northern boreal forests cause the carbon dioxide cycle to "breathe" in and out once a year -- this is the famous
Mauna Loa Carbon Dioxide graph; showing the annual cycle in red:
You've got one guess as to what the blue line is.