Let's take a different example, to maybe help with approaching the questions around roles, responsibilities and boundaries in a less heated way...
I work in the Higher Education sector. I teach upwards of 1000 students across various degree programmes and am an allocated academic tutor for around 150 of them. As an academic tutor, I am responsible for monitoring and supporting the academic development and progress of those students. The majority of students now have mental health problems. All our students have access to online and telephone/text message mental health support 24 hours per day, every day of the year. The university also has mental health caseworkers and counsellors to work with students on a referral basis (with referrals needing to be approved by Student Support). All of these are free of charge for the students. Whilst I care about my students and their wellbeing, I am not a trained counsellor or psychotherapist and cannot provide the sort of support needed if there are issues such as unwanted pregnancies, sexual misconduct allegations, trauma, or even normal mental health conditions beyond mild depression and anxiety. It is not unusual for students to want me to solve all the issues in their lives for them, but I have responsibilities for maintaining appropriate professional boundaries and am aware that not doing so could be very damaging for both students and myself. I can sympathise and signpost students towards appropriate support (both within the university and through organisations such as Cruse, Crisis, Refuge, Women's Aid, Victim Support), and will do Student Support and/or safeguarding referrals when appropriate, but that is the limit of what I can realistically do. Every year, I get students who are not happy with this and who want me to provide whatever they think would help them, rather than their being willing to engage with Student Support or the mental health support which is available to students and provided by people with the specialist training and skills needed to support them effectively.
Students with declared mental health problems are entitled to apply for a Disabled Students Allowance (DSA) which, depending on their needs assessment, typically provides between 1-3 hours of specialist study skills and mental health support per week from a trained mental health coach. Once this is approved, students need to contact the relevant department to set this up. They are all over 18 and things need to be set up by them, or by their named advocate if they are unable to do it themselves. I cannot set it up for them and, due to confidentiality and GDPR rules, that department is not allowed to speak to me about students (they can only speak to the student, their advocate or to student support). I am increasingly getting students who do not set up their DSA support, and who expect that I will provide the support for them on demand instead, because they feel that they should have the right to choose exactly what support they receive and from whom. My taking on this specialist mental health work would be unfair on the students needing the support, unfair on other students who I have responsibilities for, and unfair on myself. I do not have the specialist skills and training needed and, however well-intentioned, I could actually do a lot of damage to them by attempting something which I know I am not equipped for. Moreover, if I agree to provide that sort of individual mental health support to one tutee for e.g. 2 hours per week (something which would be done in my own time and not as part of my job), I would need to be prepared to do the same for the other 80 or so with declared mental health problems. I would be completely burnt out within a couple of weeks, and then would be of absolutely no use to any of them. There are times when recognising that you are not the right person for something, or that you are out of your depth with the support needed, is actually the most caring and responsible approach to take.
I try to set clear boundaries and expectations, and provide information to all my students about how they can access mental health support. However, it is not uncommon for students to still have very unrealistic expectations of the support I 'should' be providing for them. I get students who make complaints to the university for things like my not telephoning them immediately when they emailed me at 3am wanting help with an assignment and that causing them mental distress (they will literally email at 3am and then be on the phone to student support at 8am complaining that I haven't answered their email or phoned them). I had one last year who made a formal complaint because I had "made her suicidal" by not answering emails on Christmas day. All students had been informed in advance when the Christmas closure period was and that I would not be working or checking emails during that period. My email had an out of office reply on it which reminded students that the university was closed between 4pm on 24th December and 9am on 2nd January, stated that I would not be checking emails during this period, and outlined how to access mental health support whilst the university was closed. This should have been reasonable, but in the student's eyes I was being completely unsupportive by not being available on demand on Christmas Day. There are, unfortunately, situations where nothing we do will ever be good enough.