Why do only some aircraft require tail anti-icing?
Some airplanes don't need the horizontal stabilizer to have anti-ice because it was shown during flight testing that there were no adverse effects from having ice on the tail.  

This is mainly because the horizontal stabilizer/elevator has been designed so that even with a degradation of lift due to the ice, it still produces a sufficient tail down force to maintain control, even when approaching the stall speed.

The airplanes that do have anti-ice usually either have smaller horizontal stabilizers or (on some older designs) couldn't get the FAA to sign off on a design without it.  Some designs are also more prone to collecting ice (based mainly on the radius of the leading edge) so must demonstrate sufficient handling qualities with even more ice, which may not be possible.