Actually they do. The notion of the soul is misunderstood in in last few generations.
Every living being has a soul. You can make it more tangible by pondering on the old definition of death as separation of soul and body. The dead tree is soulless. Or in other example - your soul is everything in you what is not you body. The other name for soul is psyche/subjectivity/me (like in psychology).
There are three basic types of souls - rational like the ones of men, aware but irrational like the ones of animal, and vegetative like the ones of plants.
Since the life and soul is a special gift from God, there are moral rules extended to living animals and maybe even to plants.
But you are right in feeling that Redcloak's analogy is not appropriate - the lumber is corresponds to the human body parts and not to the personal activity which constitutes the labor.
While I don't subscribe to it, I respect your view of nature, but I fear that the youth may confuse it with Druidism. I would guess that you aren't an animist, and your beliefs protect you from the depredations of paganism and other similar superstitions.