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Burning trees that will grow back does not add any CO2 to the system, only just temporary. The trees that grow back will take up the CO2 again.This is stunningly illogical nonsense. There is no closed system [containing only trees and their CO2; the planet with all its molecules is probably a closed system], trees will happily grab any CO2 in the atmosphere regardless of where it comes from.
If you burn all the trees, none will grow back and all the CO2 will eventually be elsewhere (possibly, but not necessarily in other plants).
If you don't burn any trees, but instead cut them down to use them for building houses, new trees might grow using CO2 from other sources.
If you plant more trees without burning any, they will happily use all this evil "added" CO2 to grow.