you are missing the point...
...are plastics "live"?
...are fertilizers "live"?
...are synthetic vitamins "live"?
These are cases (there are many other examples as well) where man has "interfered" with the carbon cycle in order to create a "product".
Seems to me that you do not understand the "carbon cycle"... or any cycle for that matter at all. Or, if you do, your understanding is limited.
In addition, you seem (to me) to think in "fixed" states.
Nothing exists in a "fixed" state and everything given enough time will break down.
One needs to understand specific "fixing" bacteria and the essential\vital rolls that they play in order to fully understand these "cycles"... and much of this "science" is in its infancy... though many have suspected and hypothesized about it for eons.
There are plastic eating bacteria and plastic producing bacteria... bacteria that thrive on certain minerals\elements, etc.
Think a bit... what rolls would these bacteria play in the cycles?
Why is "science" so interested in them?
Everything you ingest in one way or the other including through your breath or skin determines the species of bacteria your body will support...
What species of bacteria do you want to support?
Did you know that the type of bacteria your body supports has a direct correlation\influence upon your weight based upon the bacterial actions on the types of foods you eat, the air you breathe and what you choose to put on your skin?
This is one reason why recent studies have found that there is about a 30% weight difference between those who eat the same number or calories per day from the same foods which are either cooked for the "heavier" group or raw for the "lighter" group.
I am offering you some valuable\vital learning opportunities here... I hope that your "knowledge" does not cause you to shut down and fail to grasp them.