Why are CJ2+ Anti-Ice & De-Ice Systems separately controlled?
Because they do two different things.

To quote FlightSafety's CJ2 Pilot Training Manual:


  Anti-ice protection systems are incorporated into wing, engine
  components, windshield, pitot-static, and angle-of-attack systems, and
  pylon ram-air scoops.  These systems should be activated prior to
  entering icing conditions.
  
  The tail deice system consists of pneumatic boots on the horizontal
  stabilizers.


Basically, anti-ice is used to prevent ice from forming in the first place on the protected surfaces of the aircraft.  This is done where it would either be "bad" to have it form in the first place (pitot-static, angle-of-attack, etc.), or where it would be "bad" to have the ice come off after it has formed (and then go through an engine, etc.).

Deice is used to remove ice after it has formed.  In this case it is used on the tail which a) isn't critical if it has a little ice, and b) the ice can be broken off after it has formed and it will just fly off the back of the airplane without damaging anything.

Since they serve two different purposes (and protect different parts of the aircraft), there are two different controls/switches.