Well I can answer two of those questions. I just said I couldn’t explain where all the oxygen came from in the first place. That’s a geologist or chemists job.
Is it true? Yes.
What happens to the carbon you breathe out? It mostly gets cycled. The carbon you breathe out is absorbed by various processes. Most of it probably gets dissolved into water in the ocean. From there it can either chemically combine with inorganic minerals and get lost more or less for good. Or it can be utilised by plants during photosynthesis. Or of course it can be absorbed by plants on land.
The plants combine the carbon atoms t produce sugars and various other substances. Most of these sugars are burned rapidly, within a few days and the carbon is released as carbon dioxide again.
See, plants respire just like animals do. Although plants do ‘breathe carbondioxide and produce oxygen’ they also ‘breathe oxygen and produce carbondioxide’, which is something that is often glossed over in high school biology for some reason. The plants use sunlight to produce sugars, but they then burn those sugars to provide energy just like animals do. It’s simply a way of converting solar energy into chemical.
During daylight hours the amount of sugar being produced is greater than the amount being burned. However as light levels fall the amount of sugar being produced falls and eventually ceases, while the amount being burned remains far more constant. As a result the plant becomes a net oxygen consumer and is busily producing carbon dioxide.
The carbon dioxide plants breathe out simply enters the cycle just like the stuff you breathe out.
The small amount of sugar that isn’t burned ad converted back into CO2 immediately to provide energy for the plant gets converted into the plant body. It is transformed into starch, cellulose, fats, proteins and all the stuff that plant are made of. As the plant body is shed in the case of limbs and leaves it begins to rot. The bacteria and fungi burn the wood and ‘‘breathe oxygen and produce carbondioxide’, releasing the carbon back into the atmosphere. When the plant dies the roots and trunk suffer the same fate.
The carbon dioxide plants breathe out simply enters the cycle just like the stuff you breathe out.
Some of the plant is of course eaten by animals. This includes you, and this is where all the carbon you breathe out comes from. They break down the plant material into carbon dioxide.
The carbon dioxide animals breathe out simply enters the cycle just like the stuff you breathe out.
Many plants and plant parts are burned in forest fires, barbecues etc. The fire converts the plant body into carbon dioxide.
The carbon dioxide animals produced by fires simply enters the cycle just like the stuff you breathe out.
So you see, you don’t produce any carbon at all, nor do you consume oxygen. You just act as a carbon conduit between one plant and the next. You prevent the plant from storing carbon by ensuring that it is all converted to CO2 and ready to be used by the next plant. Bacteria, fungi and fires do the same the same thing.
Mature forests can’t produce oxygen for this reason. The oxygen only exists until it is recombined with carbon, and that happens as soon as the tree decays or is eaten or burned. In other words the forest needs to exist as a solid in order to keep the oxygen as oxygen rather than CO2. In order to produce oxygen the mass of the forest would need to be increasing, which it clearly isn’t in a mature forest.
The only way to get s forest to produce oxygen/store carbon is to cut it down and let it regrow. A growing forest is of course increasing in mass and so producing oxygen. Provided the forests products aren’t eaten or allowed to burn or decay the forest will be genuinely producing oxygen.
Rather ironically for conservation groups one of the best ways to do this is to pulp the forest for newsprint. Most papers end up in landfills, ad once buried decay essentially ceases, with the paper very, very slowly becoming peat. The oxygen is then never recombined with carbon.
This is a potted version of a very complex biogeochemical cycle, and ignores a lot of important carbon pools, like the soil and ocean sediments, but hopefully it answers the question.