Through the correlation between Stephen and Icarus, Joyce was referencing the overconfidence and pride that both Stephen and Icarus had. It is apparent that Stephen is proud yet pretentious especially when conversing with his friends who he feels he has outgrown mentally. Icarus fell to his death because of his overconfidence and pride. This demonstrates Stephen's willingness to take risks to realize his destiny even if it includes failures.
Stephen compares himself to Lucifer in chapter four saying, "The snares of the world were its ways of sin. He would fall. He had not fallen yet but he would fall silently and in an instant." Lucifer fell from heaven because of his pride saying, "I will not serve". Stephen also full of pride in himself refuses to honor or serve his family, church and his country. This defiance in Stephen demonstrates his strong will to do what he wants with his life.
Joyce has used birds as a literary device in "A Portrait of the Artist as a Young Man" to develop themes and evoke a visual image for the reader. Birds are usually associated with freedom and flight, yet the earliest mention of birds is related to punishment. Dante's threat that eagles would pick out his eyes essentially comes true in a symbolic sense. Stephen becomes blinded by mortal sin with prostitutes and was then blinded by a life of total devotion to religion.
Heron, Stephens boyhood adversary has bird-like