The secure email system is not like opening up a second version of Outlook on your PC, they are usually stand alone terminals that are specialized to do one thing, keep the information they are transmitting secure.
So in this case there were actually 3 email systems in play.
#1: Clintons private server with all kinds of security flaws.
#2: The standard State Department email system (the .gov email address) which while mostly secure, has internet access and is therefore not permitted for high level classified materials either.
#3: SIPRNet, the real secure servers which are not connected to the internet and are used for actual classified materials (including top secret).
Various agencies have had their own internal severs hacked but SIPRNet data has only been leaked by people with direct access to a connected terminal (Chelsea Manning).
One of the issues here is that SIPRNet data was found in some of Clinton's emails and the only way for that to happen was to have someone transcribe it from the secure terminal in her office to the standard State system.