Willy has always dreamed that his son would be successful in a social and materialistic way. Because Biff has always been good looking and physically adept, Willy assumed that Biff would earn great recognition in the world and, in essence, be everything Willy wanted to be and wasn't.
When Biff mentions Bill Oliver, Willy gets excited because he sees a way that his dream for Biff can still come true. Willy latches onto the idea that Bill always liked Biff, and assumes it is possible for Biff to get a large loan and start his own business. Willy ignores Biff's lack of experience and/or know-how and just assumes that, given the right resources, Biff can accomplish anything. Happy helps to fuel the fire because he himself is desparate for his father's attention. Happy is the one to actually mention Bill Oliver in the first place, and to agree with his father's dream that the boys could take over the business world.
Biff and Willy fight, though, when Linda tries to put some caution and sense into the conversation. She tries to point out the problems with the plan, but Willy yells at her for interrupting his words of advice. Biff gets angry at this, and yells at Willy for yelling at her. Willy stops dreaming at this point and heads off to his bedroom.