Cutting down trees only helps the environment if the trees that are harvested are replaced with new plantings (even if these are not on the same site).
As trees grow, they absorb carbon dioxide through the process of photosynthesis.
The carbon dioxide absorbed by the growing forest remains stored as carbon within the wood products after the tree is harvested and remains stored throughout the lifetime of the product. (Wood is 80 percent carbon.)
If another tree is planted when the first tree is harvested, this will absorb more carbon.
At the end of the wood product’s lifetime when the wood decays or is burnt as fuel the carbon is released back into the atmosphere as carbon dioxide. If, however, the wood is properly buried at the end of its life, most of the carbon content of the wood will remain underground indefinitely.
NZ Wood - The Carbon Cycle