Why does Cole want to knock a nest of baby birds from the tree?

Cole is angered by the love and care with which the mother bird cares for her babies, something he's missed in his own life. Thus, he wants to destroy the nest.... and the family.

Up there on a branch, barely spitting distance away, little sparrows rested dry and warm , having food brought to them in the comfort of a nest built by their mother.

The sight of the baby birds irritated Cole. Without his injuries, he could easily have crawled up and knocked the nest down. That’s what the stupid birds deserved.

After feeding, the mother flitted to a branch near the nest. She ruffled her wings and chest feathers, keeping an eye on her young. Watching the bird made Cole curse every second of his miserable and haphazard life. If he were the mother bird, he would just leave the babies to fend for themselves. She didn’t owe them anything.