You may have seen diagrams of the tidal force of the Moon on the earth (like this one: https://www.oc.nps.edu/nom/day1/tide_force_diagram.gif).

Intuitively you would think that the tide is being formed because the Moon is "lifting up" the water at the point closest to the Moon. But this contribution is actually very miniscule to the tidal effect. Instead the bulk of the tides are produced about 45 degrees away where the tidal force is parallel to the Earth's surface. This has the effect of dragging the water closer to the tidal bulge.