Is wood not a carbon store?
In 2014, use of wood products in all notable categories combined was about 1.25 billion tons [3]. Including just sawnwood and wood paneling, it was 0.827 billion tons. Since there's no plausible way to use 2500% as much lumber for structural purposes as we do now, and just harvesting wood and leaving it outdoors will lead to decomposition on short (decades) time scales, people consider charring it and/or burying it underground. Just building more structures out of wood is barely going to put a dent in the problem.
Likewise, dynamically shifting the equilibrium toward wood from CO2 doesn't help much if the wood persists for only decades. The time scale for CO2 to naturally return to its pre-industrial equilibrium is more like 100,000 years [4]. We need sequestration measures that prevent CO2 from returning to the atmosphere over longer time periods than wood takes to decay naturally.
[1] https://www.statista.com/statistics/276629/global-co2-emissi...
[2] https://en.wikipedia.org/wiki/Cellulose
[3] https://www.forest2market.com/blog/fao-report-highlights-res...
[4] https://www.amazon.com/Long-Thaw-Changing-Climate-Princeton/...
1. They are only a net store of carbon while they're alive.
2. Because of that, you need to dedicate land to carbon-capture forest, indefinitely.
3. Burning fossil fuels for energy releases more and more carbon into the atmosphere.
Like, you get N tons of carbon captured out of a given land area. It's constant per area. So you would need to continually grow the amount of forested land just to follow the amount of carbon released by burning fossil fuels.
But: land is finite. The actual worldwide trend has been to deforest land, either for lumber, or slash-and-burn for subsistence farming in poor countries, or just to allow for population growth, or the large land area needed for wind and solar farms. We don't have a huge surplus of not-yet-forest land — can't grow trees in deserts.