Trees and plants are net consumers of CO2 when they grow, but become neutral when they reach maturity, so they are more of a carbon buffer. The buffer can be freed when they burn or rot, both of which happen naturally.
The best way to permanently take away CO2 from the atmosphere is to cut off the trees and somehow store them where the CO2 cannot escape (and to free space for new trees to grow). Some of the carbon from dead plants is stored in the soils, but this takes a lot of time to do.
In the long run biofuels + carbon capture can be carbon negative.
I really don't understand this logic. The oil industry spends billions every year to extract oil (= fossilized biomass) buried deep underground, because burning biomass gives you cheap energy.
If you cut down and store enough trees to compensate for the current CO2 emissions, you will have access to an immense volume of biomass, much easier to "extract" than oil is. What do you think is going to happen with this biomass? People are going to burn it to make cheap energy again..
Actually, why would you even go through the trouble of cutting down the trees in the first place? You could just, not extract the oil and end up with the exact same amount of energy you will have at the end of this complex process.
You want to use oxygen from the atmosphere, and bury it underground?
¹ Some uses for wood, like as fuel, release the carbon back into the atmosphere. Likewise anything where the wood decomposes.
Now, compress it under great pressure and heat and enter the Diamond Age.
I would argue that the first step would be to combat deforestation.