I'm not a hero
In its immediate narrative context in Telemachus, “I’m not a hero” refers to Stephen’s morbid fear of water and to his nonaggressiveness more generally. But it also constitutes a pointed reference to his original fictional name. When Joyce stayed with Gogarty in the tower he was working on a book called Stephen Hero, a long and eternally unfinished autobiographical novel whose materials Joyce eventually reworked into A Portrait of the Artist as a Young Man. The title does not imply straightforward glorification of the protagonist. Ellmann speculates that when Joyce sought a new one, it was “because he felt the first title might imply a more sardonic view of his hero than he intended” (193).
As he changed Stephen Hero into the Stephen Dedalus of A Portrait and then the Stephen Dedalus of Ulysses, he nevertheless subjected him to harsher and harsher treatment. At the end of the first chapter of A Portrait, Stephen is hailed as a hero by the other boys at Clongowes Wood College, and carried in triumph like a Roman conqueror, because he went to the rector to protest an unjust beating at the hands of a priest whom the boys all fear. But he learns later that the incident was a source of amusement to the rector. After that point he cannot take leadership seriously, even when other boys look up to him or when the priests admire his piety. In Ulysses, the question about Stephen seems to be not whether or not he is a hero, but whether or not he is a total failure.
In a letter written to his brother Stanislaus from Pola in 1905, when he was still busily working on Stephen Hero, Joyce declared, “I am sure however that the whole structure of heroism is, and always was, a damned lie” (Ellmann, 192). He did not change this opinion. The hero of Ulysses is Leopold Bloom rather than Stephen Dedalus, but Bloom is decidedly an anti-hero by the standards of ancient Greek epic. Heroism of the type exemplified by athletes and warriors is subjected to ironic scrutiny throughout the book, and made utterly ridiculous in Cyclops.