Earlier quoted context omitted.
Say you are implementing a self-tracking objects model for data management. How do you fix the reversal of control required to manage that? Specifically you need to go from the representative object to the controller to store the fact that you changed.
Weak ptr/reference. Also I would say that it's very uncommon to do/need something like this so it shouldn't be cited as an reason for cycles to be generally handled.
I have done weak pointer logic, it is not pretty.