Why is water only coming through the handheld hose?
You are correct in the fact that water is always present in the hose.  When you turn on the faucet water gets sent through a diverter valve, this valve splits the flow of water between the faucet and the hose.  It detects changes in pressure and adapts the flow accordingly.  If water is not flowing through your hose and it does not go back to the faucet then you most likely have an issue with your diverter.