User blog comment:The5lacker/Varus is not a normal AD carry/@comment-4888212-20130613135936/@comment-5266525-20130613185159

"Why, OH, WHY you would deal greater damage with AA's building AD rather than AP?"

Because AD has crit.

It really is that simple.

Also, that Thornmail won't be hurting so much after you get some lifesteal, which is another luxury that AP Varus (or any other onhit attacker for that matter) doesn't have.