In the days of early, square-sailed ships, being pushed by the wind was the only choice. Even today, there are two situations when the sail does work by direct pressure instead of lift:
on a run - also known as sailing leeward or downwind. This is where you often see that memorable, balloon-shaped sail, the spinnaker.
on a beam reach - sailing at a right angle across the wind. In this situation, the boat benefits both from direct pressure and from lift. This makes it the fastest point of sail.