Consider all of the prompts (emotional, familial, psychological) that prevent Eveline from making the decision to leave home.
Eveline is weighing the pros and cons of leaving home. It is a difficult decision for many reasons. First of all, she would be leaving the only place (and people) she knows well; she'd be leaving everything that is familiar. However, despite that familiarity and the comfort that comes from familiarity, her home life is not ideal. In fact, it seems to be quite depressing and increasingly so. Eveline gets nostalgic thinking about her childhood when her mother was still alive and her abusive father was "not so bad." So, even her nostalgia is marked with melancholy.
It would seem clear that leaving home holds more promise than staying. But Eveline is afraid of the unknown and this makes her second guess her decision to leave. There are expectations of women, at this time in Ireland, that leaving home in this way is more appropriate for a man than a woman.
In short, Eveline is conflicted and unsure about whether or not she should leave. Her home life is certainly a relatively bad one, a hard life, but sense of familial duty and fear of the unknown make her consider staying home -- even if that means having a difficult and unrewarding life as her mother did.
Frank represents not just a mate but a means of escape. Her father has forbidden her to see him. Even though it seems obvious that Eveline should be bold and go away with Frank, her fear and sense of familiarity in nostalgia for her family and homeland prevent her from making that bold decision. She even begins to rationalize staying home by thinking of fond memories of her abusive father:
Not long before, when she had been laid up for a day, he had read her out a ghost story and made toast for her at the fire. Another day, when their mother was alive, they had all gone for a picnic to the Hill of Howth. She remembered her father putting on her mother's bonnet to make the children laugh.
These thoughts creep into her head when her mind should be filled with excitement at seeing a new continent and making a new life. But she feels bonded to the familiarity of her home and then she remembers promising her mother to keep the family together. That adds guilt as a factor (or prompt) contributing to her inability to leave home willingly.
Thank you very much.