If an array contains n different items, these can be arranged in n! permutations. To sort an array, you must know which of the n! possible permuatations yu started with.
So you start with n! possible permutations. With one decision, in the best possible case n! / 2 of these permutations will give an answer "yes", and the other n! / 2 of these permutations will give an answer of "no". So with one single decision, you can reduce the possibilities from n! to n! / 2.
With k decisions, you may be able to reduce the possibilities to $n! / 2^k$ possibilities. You need to reduce the possibilities to only one, and for that you need to make at least $log_2 (n!)$ decisions.
With fewer than $log_2 (n!)$ decisions, there must be at least two permutations where all those decisions would give the same outcome, and since you don't know which of these two permutations you started with, you can't sort both permutations correctly.