Why does the question $$Are you a liar?$$ not work?

Multiple Choice

The incorrect conclusion that the cannibal is one who always tells the truth will be made if the answer is $"$no$."$

Both types of cannibals will answer $"$no$."$

The incorrect conclusion that the cannibal is one who always tells the truth will be made if the answer is "yes."

Both types of cannibals will answer with "yes."