For example when the author picks "parents" or "children" or in general maybe any entity of any kind, I don't understand what functional thinking gets me. Sure instead of manipulating mutable objects I can think of every entity being 'one thing' at 'one moment in time' and I do a gazillion state transitions that all return new things and I have never mutated anything, but not only is that bad from a performance standpoint, I never understood how that's clearer or easier, it just seems like a tortured metaphor.
Monads and other functional tools are being brought up in this thread as well but I always had the same problem. Sure, I can stuff my operations into a box, say it's the "state box" and then everything is neat but for what purpose? I still remember when I was in university I rewrote a tetris clone I had made into Haskell. It took a lot of time and weird error messages, but at the end of the day translating all my imperative or object like procedures into functional paradigms didn't make the program any easier to understand.
The places where I think functional programming is natural is for something like accounting, data processing or version control systems. Where I really do want to think of every state as its own, immutable little world, where keeping track of changes pays off, and so on. In a lot of domains it to me seems ill-suited.