Why a retraction from a building to an apartment is not isometric?

Question

Let $X$ be an affine building and $\mathcal{A}$ a system of apartment. For any apartment $A\in \mathcal{A}$ and a chamber $C$ in $A$, let us consider the retraction $\rho=\rho_{A,C}\colon X\longrightarrow A$. By the definition of $\rho$, for any object $A'$ of $\mathcal{A}$, the restriction $\rho\vert_{A'}\colon A'\longrightarrow A$ is an isometry such that fixes $A'\cap A$ pointwise. It is well-known that the retraction $\rho$ is a distance-decreasing map. For any $x,y\in X$, we can find an apartment $A'$ such that $x,y\in A'$. Then we have $$ d_{X}(x,y)=d_{A'}(x,y)=d_{A}(\rho(x),\rho(y)). $$ Here the first equal is following from the definition of metric on $X$ and second is $\rho\vert_{A'}$ is isometric. Perhaps this argument is wrong, but I'm not sure what is incorrect.