What is the US FAA concerned about when it comes to psychiatric medications?
The FAA is concerned that individuals taking anti-depressant medication will not have the mental focus required when juggling multiple tasks in real time in the cockpit.

anti-depressant medications are psychotropic -- They are specifically intended to alter the takers' mental state.  The assumption is that any artificial modification of mental state will negatively impact aeronautical decision making. 

The SSRI special issuance protocol requires, among other things, the applicant to demonstrate the ability to quickly and accurately perform multiple tasks simultaneously.  The idea is to make sure that you aren't being slowed down by the medications to the point where you can't make the right decisions rapidly enough to ensure safety of flight.