Gamers who prefer playing as either a Mage or a Healer in World of Warcraft will agree that wearing a robe and a tabard at the same time will give their in-game characters a silly look.
Technically, it's a graphical glitch in the system. We say "technically" because Blizzard is fully aware of this problem but maintains that it was actually a technical decision due to system limitations.
Community Manager Drysc explained this full at the game's official forums:
The way our armor and animation systems work, of which I will not pretend I have any knowledge of, would make it extremely difficult and labor intensive to have the tabards show properly over the robes and actually look right/good.
Something like having to change the entire system as well as remodel every piece or robe armor or some-such.
So until Blizzard comes up with a revamped setup for World of Warcraft, Mages and Healers would just have to choose between the two clothing or wear them together and try not to look funny around Azeroth.