In order for teams to manage themselves, they need to be dependent on one another for direction. They can not look to the ScrumMaster or Product Owner for direction or orders. The team uses its abilities ranging from subject matter expertise to best gut instincts to make its own decisions. It is very much like a sports team where everybody has a role, but the team wins games as a team, not as individuals. In Hockey, you get the same amount of points for an assist as you do for scoring a goal and it is the same in work.
The reason Scrum and stand-ups never worked at my old job was because "team" members were pitted against one another. It was a Lord of the Flies, survival of the fittest, where progress was always reported to some kind of boss man. No one in the group ever had a stake in the success or failure of the work other team members were doing. It was much more like a World Rally Cross event, where team members all drove Subarus but were conducting their own race, competing with each other to win each stage of the rally. It was awful.