Pressing the spout (faucet) and water does not flow or flows very slowly

For systems with tank - check if water supply valve or tank valve is open or whether the tank is not empty.

For systems without tank - check (by unscrewing the spout) whether water pressure in your pipes is sufficient. If it is, the reason for the slow filtration of water migjht be clogged pre-filters or worn diaphragm

Other causes: lack of pressure at the bottom of the tank, used cartridges or osmotic membrane.