A primitive element in $F_2$ cannot contain both $x$ and $x^{-1}$

Question

Suppose $w$ is a non-empty cyclically reduced word in the alphabet $\lbrace x,y,x^{-1},y^{-1}\rbrace$ and that $w$ represents a primitive element of $\langle x,y\rangle\cong F_2$. Why is it that $w$ cannot contain, say, both $x$ and $x^{-1}$? I can't find a source on this that doesn't delve into the fully general case of $F_n$. I am not super familiar with group theory, and I just want to understand why this specific statement holds. Thanks!