I find all the perspectives in this thread really interesting. What really caught my eye about the original question was not really should we have sympathy for one another-- which seems to have become the focal point of the discussion, and maybe rightly so...
But there's one aspect to the original question which I think also needs to be asked, which is, should we have sympathy for one another because we have disorders.

To use this site as an example, not exactly everyone who comes here exactly interacts with each other on the basis of their "illness." I think one of the reasons this site works really well is actually, despite the fact it is split up on the main page as categories of "disorders," the focus is not generally on unwellness-- I actually don't see a lot of this, "I'm depressed, help!" stuff. However, I do think that having an open forum to talk about disorders-- no stigma-- helps people to share their experiences and be open about them. And that in turn encourages others to be supportive and helpful.

I'm not convinced that disclosing "disorders" in real life always encourages others to be supportive and helpful, which is the only thing I have against labelling mental suffering.