Symbolism, Imagery, Allegory
As a symbol, the boy is a little more straightforward than the tree. Regardless of how you choose to interpret the book, the boy pretty much always represents the same thing: man, or humanity. Exactly how he represents man (or humanity), however, varies a bit depending on your reading of the book.
The Unhealthy Relationship Angle
If we go with the codependent, dysfunctional relationship interpretation, the boy represents an abuser. He takes what he wants from the relationship without giving anything back, and he's so selfish that he causes harm to his partner. Indeed, he cuts her down—quite literally—until she has almost nothing left. And then he sits on her.
We have no reason to believe that the boy takes joy in his abuse of the tree; in fact, nothing seems to make him happy. Even so, we can't really pity him in this scenario since he's the one perpetuating the abuse, and he never takes responsibility for his actions.
The Careless Consumption of Nature Angle
In an environmental reading of the book, where the tree represents nature and the boy represents (again) humanity, we see another kind of dysfunctional relationship. Here, the boy also takes and takes without thought of the consequences of his actions. The end result: no more tree—just a stump—and no satisfaction for the boy…or humanity.
The Parent-Child Relationship
Sure, kids are supposed to depend on their parents, but as a representative of the child in the parent-child relationship, the boy does a lot more than depend. He bleeds the tree dry.
Like a child who never quite leaves the nest, the boy is a continual leech on the family resources, and he doesn't stop until there's nothing left to take. And then he still comes back for more.
In Summary
No matter how you slice it, the boy comes off looking bad.
Sure, we can feel some level of sympathy for him because in the end, sitting there on the stump with his shoulders stooped and his hat on his knee, he looks pretty pathetic. But all in all, he's not a very likable character.
In every scenario, he starts out happy and winds up miserable—and it's all because of the choices he makes. With this in mind, we think it's fair to say that overall, the boy as a symbol of man and humanity shines a bright light on the challenges of being human and finding happiness. He's also a prime example of what happens when one lives a life of shallow self-interest instead of taking time to appreciate and care for others—or the environment. Or both.