1.) If you plant a commercial forest and then cut it down and burn it entirely.
2.) In the cosmic sense that all atoms will return to dust at some point.
In all other scenarios the statement is not helpful in particular because:
1.) Climate change is happening right now and is an acute global crisis which requires extremely short term measures (on an geological time scales). Growing a forest right now, captures carbon now when we need it most.
2.) If you cut down the trees after some time, you can actually just stack the trunks and they will most likely just be inert for a long time. The number of fungi and beetles that are specialized in dealing with decomposing wood is surprisingly low. In comparison to Carbon Capture technologies, which try to capture carbon from air and then store that somewhere, using trees is extremely easy.
Even worse, a focus on tree-planting often feels like an inconsequential feel-good movement, that deviates attention away from the real problem: that every year we are unearthing millions of years worth of captured carbon and putting it back into circulation. Growing a forest while we burn thousands of oil tankers every year is like trying to remove water from the sinking titanic with a bucket. It doesn't harm, but it gets stupidly in the way.
As long as we don't remove fossil fuel usage, planting trees is just something to make us feel better without actually fixing the problem.
Also, you can plant as much as you want, it's going to be much less than what's burned by planters in amazon's forest alone, and they are actually burning the wood.
The main take-away is that destroying something is always several orders of magnitude easier than building that thing, and as long as we don't stop destroying we won't manage to build at a faster rate, therefore stop deluding yourselves.
Thankfully the amazon reclaims farmland at a scary pace if left to its own devices.
In fact, a well built log house can last for hundreds of years if maintained properly. We have plenty of those with original wood from 1800's. Wood can be used to build larger buildings as well.
No. They liberate very little.
Bury or sink wood and it will stay put.
Why? plants are carbon neutral. They capture some carbon while they live, then liberate all that carbon when they die and are decomposed. No carbon ever leaves the biosphere.
Carbon capture would happen if you cut down a whole forest (regardless of who planted it) and buried it a few miles underground, sealing the mine. That way the carbon leaves the biosphere.