Longest Common subsequence theorem in CLRS
The theorem is used to construct a recurrence relation for computing the LCS of $X$ and $Y$. The first point states that if $x_m = y_n$, then one possible LCS of $X$ and $Y$ is an LCS of $X_{m-1}$ and $Y_{n-1}$ together with $x_m$. This is one of the cases in the recurrence relation.

You ask why we are not considering $Z$ as the LCS of $X$ and $Y$. There is no need to consider this, because this is already assumed to hold in the premise of the theorem. Given that, we want to deduce other information, which will later enable us to compute the LCS recursively.