> Longer lifespans cause fewer generations per time period
This is not true though. It would be true assuming a constant population size or a single offspring. The number of children I have and the number of children my children have has nothing to do with how long we live.
But, how long you live might affect how many children you have.
Think of it this way: if you knew you had a high probability of living to 80, you might decide to have fewer offspring so that you could dedicate your earnings to supporting yourself in your later years (children are very expensive after all).
Regardless of whether this hypothesis is true, clearly the number of years you live likely has some bearing on how many children you might choose to have.
This is not true though. It would be true assuming a constant population size or a single offspring. The number of children I have and the number of children my children have has nothing to do with how long we live.