Most of us are unqualified civilians and would baulk at being expected to fix a broken leg!!
However, if confronted with such, it seems many more of us are prepared to offer sympathy and support for someone with a serious fracture than are willing to do the same for a mental health issue that's often not so immediately visible.
My reaction to a broken bone would be (and has been in real life) to express sympathy for their predicament. To acknowledge the pain they're experiencing, to agree how frustrating and inconvenient it must be, to enquire how they're feeling at regular intervals and to offer practical help when I can, with lifts, with fetching shopping, with keeping the garden in check, or with running the hoover round etc. Obviously, some of the practical help is dependent upon other commitments and distance but I've always tried to do what I can in such situations, unless I've been absolutely floored by my own situation at the time, and at the very least, have kept in touch just to see how they're recovering, i.e. showing an interest in what's going on.
Each of us can only speak from our own experience, but on the very few occasions I've disclosed that I'm struggling with my mental health , I've found that that 'interest' is severely lacking. I've rarely found sympathy, nor any recognition of how poor mental health can make it all but impossible to function 'normally' and can therefore be just as frustrating and inconvenient as a broken bone. Despite day to day living feeling akin to wading through tar I have never had any offers of practical help to alleviate the feeling of being overwhelmed. The irony is, that when you suffer a fracture, there is almost always an end in sight - the majority of people go on to make a full recovery with no lingering repercussions. However painful, restrictive and frustrating a broken bone is, it'll be a temporary state of affairs. Knowing that makes all the intervening crap far more bearable for the person afflicted and you could perhaps therefore argue that the fracture victim actually needs emotional support rather less than someone with a mental health condition.
A lot of people are inherently selfish and will grasp any excuse not to put themselves out for someone else. Clearly, you can't cast (excuse the pun) any doubt on a broken leg because it's there for all to see. It's much easier to dismiss someone who's mentally ill if you convince yourself that they're attention seeking, being a drama queen, swinging the lead, or claiming to be ill in order to swerve their responsibilities. Then, you can brush them off with a clear conscience because, after all, very often the only 'proof' they have of being mentally ill is 'what they tell you' …. even if they have a diagnosis …. because, again, the doctor can 'only go on what they're told' etc etc.
I'm very aware that various MH conditions manifest themselves differently in individuals, and acknowledge that sometimes sufferers expect an unsustainable amount of support which is obviously unrealistic and utterly draining for those targeted. I've been on that side myself in the past and have wanted to run away, especially when you have the same circular discussions ad infinitum without any apparent benefit. However, as I've already tried to articulate (not terribly well) and as others have also described, I think it's so important that MH sufferers aren't completely pushed away. It's entirely possible to be suffering/struggling and still have enough rational thought to recognise that others might not have the time or emotional resources to offer you very much help …. and in that case, to protect yourself (understandably) you set firm boundaries if you have to (if feeling harassed). You decide when you want to have contact but for goodness sake, if you care about someone, don't leave them thinking that you don't because you've not spoken to them, or sent a note, or a quick text in six bloody months after they've just opened their heart to you about symptoms which can be terrifying, paralysing and/or unrelenting! I would much rather someone tell me they're busy/totally occupied with family/suffering some form of poor mental and/or physical health themselves and therefore feel unable to add to their load than them metaphorically slamming the door in my face. The first explanation suggests a lack of support isn't personal whereas it's extremely difficult to draw any conclusion from the second apart from the fact you're not cared about, not liked and so on which adds significantly to the feelings of isolation and self loathing many of those with MH issues experience.