Having each generation do better than the one before may be part of the American dream, but I think it’s important to realize that there’s a plateau level. After one generation reaches a certain level of educational, professional, and financial success, it’s likely that the next generations can only match that success, not exceed it. And in some instances they may not even match it.
If you’re a physician (doctoral level education), and your child chooses a career in engineering (which typically does not require a doctorate), is your child a failure? If you earn a very high income in business, but your child becomes a teacher and therefore earns much less, is that failure? I don’t think so.