A shuffling algorithm is supposed to generate a random permutation of a given finite set. So, for a set of size $n$, a shuffling algorithm should return any of the $n!$ permutations of the set uniformly at random.
Also, conceptually, a randomized algorithm can be viewed as a deterministic algorithm of the input and some random seed. Let $S$ be any shuffling algorithm. On input $X$ of size $n$, its output is a function of the randomness it has read. To produce $n!$ different outputs, $S$ must have read at least $\log(n!) = \Omega(n \log n)$ bits of randomness. Hence, any shuffling algorithm must take $\Omega(n \log n)$ time.