Why does cabin air have to be dehumidified?
A lot of consideration is placed on the airframe (which has to hold for 20+ years) rather than the passengers. 

One of the primary reasons is to slow corrosion of the  aluminium airframe. This is also why the Boeing 787 is a lot more humid - corrosion is no longer an issue in a composite fuselage (or a lot less at least). 

Boeing and the Economist sum it up nicely I think:



  the greatest issue lies with the cold fuselage skin interacting with
  moist air, which will condensate and speed up the rate of corrosion.


  But condensation in the gap between cabin and hull can be lethal.
  This gap contains much of an aircraft's wiring, and water can damage
  that wiring's insulation. Such a problem is thought to have
  contributed to the loss of a Swissair DC-11 off the Atlantic coast of
  America a few years ago. Too much condensation causes other
  difficulties, as well. There have been cases when ice has built up
  inside the tailplanes of aircraft, causing their rudders to freeze and
  thus preventing their pilots from steering them.


  An aircraft such as a Boeing 747-400 can accumulate as much as 700kg of condensation before it reaches equilibrium. Even though
  that is only about 0.17% of the 400 tonnes such an aircraft weighs
  fully laden, it is enough to cause problems for the pilot when he
  tries to trim the balance of the aircraft. And 700kg is about the
  weight of nine men. So the aircraft is carrying the equivalent of at
  least nine non-fare-paying passengers, in an industry where every
  extra kilogram affects fuel consumption and profit margins.