Nature can be a bit more complex.
Take baboons. Male indeed leave the troop while females tend to stay, but there is an exception. Low ranking females also tend to leave and join new troops. It is not that great to be at the bottom of the social hierarchy and female hierarchy in a baboon troop is based on linage so there is very little social mobility. Joining a new troop is not easy and often produce the same results as new females are rarely welcomed by the other females but it has a slightly better chance for social mobility compared to staying in the old one.
I would be surprised if you don't see the same pattern in many other social animals where the majority of the females are blood relatives.
Bees are a bit complex since in order to create new hives they swarm. In that situation they create a new queen and the old queen leaves with a subset of the bees and form a new hive while the new queen stays and start to lay eggs in the old hive.