@MrFakOff Look into forestry a bit. Deforestation in and of itself isn't a bad thing. You need to thin some forestland to allow for the proper growth of new trees and the long-term health of not only those newer trees but of the forest itself, not to mention the wildlife living there. You can also balance the amount of forestland you harvest per year, month, etc with how many trees you plant and are actively or passively allowing to grow anew. Also,
@hvdvyve made a good point as well. We don't know how many people in the tribe are assigned this job. It could only be him and his father before him. We also don't know the size of this fictional planet nor the size of their forestland(s). This is only what I could think of off the top of my head, look into forestry and the benefits of thinning (intelligently) forestland.