I don't have a solution, but that's the argument I often hear... is that it's discriminatory to shine a light on people with mental illness.
Then again, I also oppose keeping firearms out of the hands of those with mental disabilities and a history of non-violence.
Once you make another list, it becomes much easier to be put on this list. You go into the doctor for something you feel is unrelated and they are now forced to report your name to whoever. Thats the main concern.