(non-teacherly but service-role-orientated feedback) Professional detachment is a really good idea, I think. It does not mean caring less, or necessarily being unavailable, or denying extras. It means placing a mental reception-desk between your pupil/pupil's parent/client/whatever and yourself. Instead of standing there as an unprotected, vulnerable human talking to a demanding parent asking for the impossible, you are standing as a professional behind a professional reception-desk with a metaphorical cheese-plant and a pile of Readers Digests in the waiting room. They are getting a professional service about which you care very much. You are the professional. They get to interact with you professionally, and you will give them top-notch professional advice, arrange your work with them to the best standards - but they cannot attack you as a private individual (I don't mean they can't try; they will! But it won't work because your thinking will be that of a receptionist fending off a bad customer rather than the thinking of a private individual who's being bullied), and when you go home (even if you are teaching in your own home, you should "go home", in that at some point the students are gone, the work day is over, and you are home) - you leave your work behind for the next day. You can choose to do extras, like you'd choose to work overtime, but it's a professionally-made choice, not something foisted on you by your human vulnerability to pushy people.
Professional detachment is part of taking a pride in what you do. Your mental reception desk is not only a shield against unprofessional clients, it's also a standard operating procedure for treating everyone fairly, thinking about difficult and easy students alike, in terms of "what is my professional strategy for a student in this situation?".
Frankly, having a mental reception desk is helpful in almost any walk of life. It doesn't create a bad impression, honest; people generally like calm professionalism because it's predictable.
Yes, it does give you some distance, because you can say in your head: "the situation was this; I have done the right thing; what happens next is out of my control, but I will, next week, assess the consequences and decide what the next right thing to do is" - and with that, you can (hopefully) drop the situation until next week.
That's what I think anyway, from a different part of the service-world.