Why is Mangan's sister viewed as a symbol of Ireland in "Araby"?
It may be a matter of opinion that Mangan's sister represents Ireland, but knowing Joyce, it seems quite safe to make this interpretation. The personification of Ireland is a persistent theme in Joyce's works. Notice that the boy has never really known Mangan's sister. This alone is worthy symbolism of an idealized Ireland, the only Ireland that a person of the boy's generation can know. Driving the plot of the story is a seemingly hopeless quest that the boy undertakes on behalf of this woman, or his native country. It is probably not too cynical to take the drunken uncle to represent the Irish people. And the bazaar, England herself. Every conceivable obstacle that can slow our boy's quest, impedes him, but he perseveres, only to reach his destination to a conclusion which seems utterly heartbreaking somehow if we take it in the context of the story.
If we accept the premise that Mangan's sister is Ireland, it is easy to consider the story to be at least partly allegorical. For a different view of this theme, the personification of Ireland, one that almost certainly inspired Joyce, read Cathleen ni Houlihan by W.B. Yeats.