In the following question
Example 1.7 Girondo's Introduction to compact riemann surfaces
I were asking for a parametrization of hyperelliptic curves. At a certain point, in the answer, I read the following affirmation:
"The simplest holomorphic function $\gamma$ on $D_\epsilon(0)$ with $\gamma(0)=0$ that isn't constant and has a holomorphic square root is $\gamma(z)=z^2$"
So, my question is: why $f(z)=z^2$ is the simplest non-constant holomorphic functions with the above properties and $f(z)=z$ is not?