Currently in all species I know of, each generation raises its children, who in turn raise their children, etc. This can be described as an overlapping generations model where each generation lives 2 periods, receives resources from the old of the previous generation in its youth and transfers resources to the young of the next generation when old. There is another equilibrium: each generation raises its grandchildren, has its children raised by its parents, and the children in turn raise their grandchildren. Instead of transferring resources to the next generation and receiving them from the previous, transfer resources two generations forward and receive them from two generations back. There are an infinite number of such equilibria: for each n, transfer resources n generations forward and receive them from n generations back. There are of course practical problems with large n, because the organisms do not live long enough to meet their level-n offspring.
There are complaints in developed countries that childbirth is postponed in life to acquire education and start a career. A possible solution is transitioning to an equilibrium of taking care of grandchildren, together with having children at a young age so that the grandparents are still alive to see the teenage years of their grandchildren. However, the equilibrium transition from taking care of children to taking care of grandchildren means that one generation must raise both children and grandchildren. The equilibrium transition in the other direction is easy – one generation does not raise its children or grandchildren, because its children are raised by its parents and its grandchildren by its children. Any other equilibrium is less stable than the raising-children one, because it is difficult to transition to it and easy to transition away.
The equilibrium stability comparision is similar to the social security equilibria in overlapping generations. In one equilibrium, everyone saves for their own retirement and consumes their savings when old. In another, every generation when young pays the social security costs of the previous generation who is old at the same time. The transition from the saving equilibrium to the equilibrium of paying the previous generation is easy, because one generation gets its savings and the contribution from the young, while the young do not save and receive the contribution of the next generation. The reverse transition is difficult, because one generation does not get a contribution from the young in its old age, but has to finance the retirement of the previous generation when young.