Why do sailing ships have trouble sailing at the equator?

Answer 1

It's not at the equator that the problems occur; it's a few degrees north and south of the equator. Coriolis force from the earth's rotation causes the same airflow patterns that make the trade winds in other parts of the globe to circulate up and down instead of across the surface of the planet.

These latitudinal bands, the Doldrums and the Horse latitudes, are places where there can be no wind for weeks. If you're operating under sail power alone, you can get stuck for a surprisingly long period of time.