For one, they want the government to keep a record of people suffering from mental illness.
I think to some people this may have, at first glance, some sense, but think about how this would be implemented:
If you go to a psychiatrist, you get put on the list --> people won't seek the help they need
Only put on the list if you have already committed a crime --> would not have prevented the recent tragedy, plus people who are convicted of crimes are already recorded, so all this does is stigmatize people with mental illness
The whole thing just reeks of a way for the government to stigmatize either perfectly benign people with mental illness, or people who it doesn't like for other reasons. Imagine trying to run for office against someone if they put your name on the 'mental illness list'.