Mail auto starts @ re-start computer

Apple Mail app always starts when I restart my computer. I have the app disabled. I've checked "Get Info" and there appears no way to adjust permissions for it as I get a dialog stating I don't have permission to change settings. System is set another non-Apple mail app. I tried deleting Mail and get a dialog stating app cannot be deleted because system needs it. OK, fine, but I still want the app to stop booting up every time I re-start.

I upgraded to El Capitan yesterday

My Computer: MBP/retina, mid 2012

OS: El Capitan, 10.11

Any help would be appreciated