Because that's how the Westside operates. Back then, and up until today. If you were a soldier, you knew your skipper. That's it. Simple as that. And that's the way it's SUPPOSED to be.
Certainly this would be a good way to promote secrecy, and to keep the identities of other members and higher-up's secret from low-ranking members.
However, whether from movies or from books, I thought that during initiation ceremonies many
(if not all) other members of the family, including the boss, would be in attendance and circle around the new members, who would then swear their loyalty to them