The common understanding is that a tree’s leaves die at the end of the summer, and then fall off. This isn’t quite accurate. It’s more correct to say that the tree kills its leaves.
What’s really happening is that the tree builds a layer of cells inside the leaf’s stem to create a seal that blocks the flow of nutrients to the leaf. Imagine putting a tourniquet around your arm and leaving it there: eventually your arm would die and fall off, and that’s exactly what happens to the leaf.
A similar thing happens with branches. Humans, like most other animals, start their lives with a fixed number of limbs, and don’t get any more. For this reason, we’re very interested in keeping our arms and legs intact. But a tree can grow a new limb pretty much whenever and wherever it wants. When a branch isn’t pulling its weight, the tree will kill it – by creating an internal seal and starving it to death – and then grow a new branch that contributes more to the tree as a whole.
When a leaf or branch that has been killed in this way falls off, it doesn’t do the tree any harm. The tree wasn’t using that body part anymore, and the internal seal prevents any infection from entering the living parts of the tree. In contrast, when a leaf or branch is broken off suddenly – perhaps due to a hungry herbivore, pruning, or a powerful windstorm – the tree loses a healthy, productive body part, and acquires a wound through which insects or fungal infections can easily enter. Because trees don’t do anything very quickly, it can take them years to seal even a relatively small wound – more than enough time for a serious infection to set in.
It’s therefore inaccurate to say that cutting off a tree’s limb doesn’t hurt the tree. Of course, it doesn’t hurt the tree the same way that it would hurt a human, because the tree can regenerate. But the loss of a productively photosynthesizing branch, coupled with the energy demands of sealing a wound and growing a replacement branch, can put serious stress on a tree. While pruning may be desired for other reasons, the idea that pruning is good for a tree’s health just doesn’t cut the mustard.