Movement of water molecules through the lipid bilayer is very slow due to water's molecular polarity/hydrophilic nature. While water can cross the membrane on its own, so much water has to move across membrane during the normal life of a cell that help from a transport protein is needed to provide the required speed of transport.
Work Step by Step
The key here is to see that transport is not just affected by whether a molecule can move on its own but by how much must move. This is analogous with the question in biochemistry of how quickly a reaction can proceed, not just whether it is spontaneous.