Doodle and his brother are opposites because Doodle is weak and his brother is strong, but Doodle is kind and his brother is cruel.
Doodle was persistent enough to survive even though he was born sickly. His brother was embarrassed of him from the start, and took advantage of that fact to justify being cruel to him.
There is inside me (and with sadness I have seen it in others) a knot of cruelty borne by the stream of love. And at times I was mean to Doodle.
An example of this cruelty is when he showed his brother the coffin. Their father made the coffin when Doodle was not expected to live. Brother resented this, and that is why he showed him the coffin.
When Doodle fails to learn how to row the boat, Brother resents him. That one failure is symbolic and representative of all of the things Doodle will not be able to do. No matter what he tries, he will not be able to make his brother normal.
The knowledge that our plans had come to nothing was bitter, and that streak of cruelty within me awakened. I ran as fast as I could, leaving him far behind with a wall of rain dividing us.
Doodle uses his weakness to develop a sensitivity and empathy with all living things. He cries when he sees the beauty in nature. This is a direct contrast to Brother's cruelty. Doodle goes out of his way to be kind. He even buries the bird, recognizing the irony of its making it that far just to die, even as Brother simply scoffs.
Doodle knelt beside the ibis: "I'm going to bury him."
This foreshadows Doodle's becoming the Scarlet Ibis himself, because he made it that far and then died, just like the bird.