A Unicorn horn argument is any argument that is based on
the premise 'If it helps me, it should be done.'  These
are the kinds of arguments that drive wizards to the bottle.
Some examples are:

My secondary guild should get access to every tert path.
My race should get 110% exp rate and 8 limbs.
Monsters should give 5 times the gold and experience.
My weapon should never break.

Unicorn horn arguments get their name from some line of 
argument... but we can't remember due to brain cells being
destroyed from alcohol.