In page 93 of Kunen's book, exercise 55 says:
Show that the following version of $\diamondsuit$ is inconsistent: There are $A_\alpha \subset \alpha$ for $\alpha < \omega_1$, such that for all stationary $A\subset \omega_1$, $\exists \alpha \in A (A \cap \alpha=A_\alpha)$.
I know that there is a version of this principle taking closed unbounded sets, but why we can't use stationary sets? Why is this version of Jensen's principle $\diamondsuit$ inconsistent?