I wouldn't say Bill was old money. Old money is where neither you nor your parents need to work for a living due to the success of some ancestor. Bill Gates was upper middle class, not old money, and even so is that really necessary and sufficient cause for his success? Like other posters here, I know many people more privileged than Bill Gates was and have done little to nothing with their lives, therefore coming from his parent's level of wealth is not even close to sufficient for success. There are also certain people who have made it to his level of wealth from more humble origins, notably John Rockefeller and Andrew Carnegie but more recently Jeff Bezos, who was middle class, therefore it is not necessary to come from Gate's parents level of wealth either.

If something is neither necessary nor even close to sufficient for success, how can you dismiss someone's success as due to it?