In Joyce's short story, "Eveline," Eveline is trapped and figuratively paralyzed in a bad home life. She is the responsible person in her home and takes care of her little brother and her abusive father.
Her going to Buenes Aires is an opportunity to escape. Like other characters in Joyce's short story collection, Dubliners, from which this story comes, she is a Dubliner trapped in Ireland and unable to escape. Moving away to South America would present her with what would most likely be a better life.
But this escape comes at too high a price, apparently. Dubliners features characters that don't get out of Ireland, even when they have a chance. In Eveline's case, she is in a no win situation. To leave would probably present her with a better existence, but would leave her family uncared for. She freezes when it is time to go--she is literally, and figuratively, frozen. She has no good choice. She desperately wants to escape, but cannot bring herself to do so.
It is important to note that this is sophisticated fiction. Eveline does not cheerily stay and idealistically look forward to being the rock of her family or whatever. This story presents no moral lesson. The fiction realistically depicts a woman trapped in a modern situation with no way out. It is dark and honest.
In "Eveline" by James Joyce, Eveline had many reasons for wanting to leave home and go with Frank to Buenos Ayres. One reason was that she liked him. He was kind and gentle, yet a manly sailor. At first she was just pleased at his attention but then, as she came to know him, she grew to like him.
Another reason was that in her present-day life, she fought weekly with her father about whether his and her earnings would be used to pay living expenses and buy food or whether he would spend it all on alcohol. She did all the house work and cooking for her father and took care of the younger children her mother had left behind at her death. She worked at the Stores where she was mistreated, undervalued and most unhappy.
A third reason for wanting to go with Frank was that her past experiences were sad and painful. Her father had been drunken and abusive to her mother and cruel to herself and her brothers and sisters. When they were children they had "seemed to be" happy then, but there was always the shadow of their father's violence and it was a shadowed that worsened over the years and threatened her more darkly in the present.