Not always, but being born into wealthy families generally gives you an advantage. People who are born into well-off families usually get better educations than people who are not, which gets them into better schools, gets them better jobs, etc.
Most people can't become rich in one lifetime. Not mega-wealth, that is. Few do, like Warren Buffet, Bill Gates, and the like. It usually takes several generations to build up great wealth. But then, that's difficult too because of our high inheritance taxes.