acid base - Why is CrCl3 acidic?

Why is $\ce{CrCl3}$ acidic? I know that it has a high charge density given that it is a transition metal ion, and can hence polarize neighbouring water molecules, resulting in hydrolysis and formation of $\ce{H+}$. However, I am a little confused over how this happens? Is the water molecule that it polarizes the ones that have formed a coordinate bond with it, or simply any water molecule? Also, with the high charge density, it should be attracting electrons from the water molecule. But does it mean that it attracts the 2 electrons forming the bond between $\ce{O}$ and $\ce{H}$? And if it attracts them to itself, why doesn't it form an extra coordinate bond? Why is there still only 1 coordinate bond? Another thing that I don't understand is that $\ce{OH-}$ has a lower d-orbital splitting ability than $\ce{H2O}$, doesn't that mean coordinate bonds with $\ce{H2O}$ are preferred? Why do they still polarize $\ce{H2O}$ to get $\ce{OH-}$ instead?