Willy has a tense and difficult relationship with his elder son Biff. He feels that Biff has let him down by not being any more successful in life than Willy himself has been. Biff has no proper job, is not married, and is unable to settle down to anything. Willy seems to feel that Biff has failed on purpose, just to spite his father: 'You don't want to be anything, is that what's behind it?' he accuses Biff during their confrontation in the restaurant (Act II).
What Willy does not understand is that Biff has become very confused about life. As Biff tells his brother Happy early on in the play:
I tell ya Hap, I don't know what the future is. I don't know - what I'm supposed to want. (Act I)
Biff, therefore, has no direction at all - he doesn't know what he should be aiming for.
Willy is a major reason why Biff feels like this. When younger, Biff looked up to his father as a role model - at least this is how Willy remembers it - but his faith in him was severely shaken by accidentally finding out that Willy was having an affair. Ever since this he has scorned Willy's devoted husband and father act, although evidently he has never brought himself to tell anyone else of this affair.
Even more damaging, though, from Biff's perspective, are Willy's ideas of how to get on in life. Willy has taught his sons that being popular is really all that matters, that success will follow if one is 'well-liked', rather than inculcating the virtues of study, and hard and steady work. Biff feels that this led to his failure in high school and thereafter he has been unable to apply himself to anything.
Willy's relationship with his younger son Happy is not as fraught as his relationship with Biff, but it is still unsatisfactory. Although, on the surface, Happy appears more settled than Biff, he has not turned out a success either. He is in a low-paid job, living on rent, and like Biff he has not settled down and got married, but continues to run around with various women. He vies for his father's attention, but Willy is always more focussed on Biff, his one-time favourite son, on whom he seems to have pinned all his hopes. Yet it is Happy that Willy ends up influencing the most; he shares his father's delusions about gaining success and wealth, whereas Biff is able to see through them.