Why can't a square number be prime?

Because Prime number is divisible only by 1 and itself. For example, 17 only has 2 factors - 1 and 17.

With the exception of the number 1, all other square numbers are divisible by a number other than 1 and itself. For example, 36 has the factors 1, 2, 3, 4, 6, 9, 12, 18, and 36.