The conflict between Amanda and Tom in this masterful play centres on the way in which Tom feels drawn to, as his father did, seek his fortune and discover himself through venturing away from his mother and sister and leaving them. This is a tendency that Amanda recognises very early on in the play. However, from her point of view, she tries to make Tom realise that he has a responsibility to try and help Laura and find someone that she could marry before he leaves them in what is to her a selfish manner. Note the following quote:
I mean that as soon as Laura has got somebody to take care of her, married, a home of her own, independent--why, then you'll be free to go wherever you please, on land, on sea, whichever way the wind blows you! But until that time you've got to look out for your sister.
For Amanda, responsibility is looking after those who are dependent upon you. She finds Tom's attitude to life and his desire to follow in his father's footsteps as something that is deeply selfish and irresponsible. Of course, from Tom's perspective, as is shown by the way that he uses the money for the electricity bill to buy his ticket away from his family, his responsibility is to himself first and his actions from his perspective are therefore not selfish.