Biodiversity is what nature does. It starts with soil, then small plants, and gradually you get trees. It's very energy efficient, but it's a very slow process.
Industrial monocultives are nothing like that. It's much faster, but it works out of the paths nature has. Usually by emitting CO2 directly, which impacts climate change.
For example, the natural process of building the soil of a forest takes decades of tiny plants and animals living and pooping and dying, while artificial lumber forest soil is brought in trucks, and set in a single season, with fertilizer extracted from a mine (more CO2). The pooping and dying part releases some CO2 as well, but it cannot compare.
On top of that, cultivation tends to take land from wild forests and jungles. So that doubles the effect.
Permaculture is a way to produce food and wood products using methods that mimic what nature does. Give it a look if you are interested in these things.
In the US, increased demand can be met with renewable sources of lumber. This has the side benefit of modest carbon sequestration.
Population growth is also slowing, which may actually pose a more serious problem for labor and innovation. Immigration helps, but it won't be enough.
In other areas of the world, the problem is one of economics, as the parent mentioned.
There is no way that pulling timber out of the forest and converting into a product actually sequesters anything. Hauling the wood out of the forest to the mill likely releases more carbon than is sequestered by the tree in its lifetime.
This probably not true, considering that for many decades steam powered logging equipment burned wood before coal became the dominant fuel source (and thus able to cut down and process a tree with less energy than we got from a single tree), although many mills were powered by flowing water.
It's the same notion that "PV panels emit an equivalent of 50g of CO2 per kW/h (assuming a 25 year service life)". Even though the panel doesn't emit anything during operation, mining and manufacturing are still heavily reliant on fossil fuels.
The tree itself sequesters carbon, but the carbon output from using the tree is what is produced burning it + getting it ready to burn.
On the other hand, a growing population means more demand for wood products (for building, for furniture, etc) and the alternative, plastics, are quite problematic.