The answer I was given was that the ocean isn’t perfectly flat, but has waves bouncing up and down, and these, especially when added up over distance, cause ships to appear to be “hull down” in the distance.
In the same sense, I was told that I can’t see the distant Himalayas because smaller, nearby hills block the view to these much taller, but more distant mountains. (Also, the atmosphere isn’t perfectly clear, and opacity accumulates with distance. Just as mountains appear to be blue or purple when 50 miles away, they simply can’t be seen at all at 500 miles away.)
These arguments fail when you take the trouble to make careful observations with decent instruments. You can go out to the desert, and look at long lines of electrical power pylons. You can go to places where the ocean cuts the land into large bays. You can measure the angles of stars or planets above the horizon; this, when done in partnership with friends at various distances, will quickly produce results that demolish (or at least call into serious question!) the tenets of the Flat Earth viewpoint.
Other observations require at least a little faith in humanity. You can talk to ships’ captains, or airline pilots, who have navigated vessels from South America to South Africa, or from South Africa to Australia. If the world was flat, as in the polar projection in the United Nations logo, these distances would be MUCH greater than they are on a globe.
Photographs from space, and GPS data, and other high-tech evidence, is also difficult to refute.
Hand-waving and saying “Refraction” only goes so far. Saying that NASA is part of a vast conspiracy is, alas, a pretty weak argument. (I’m not suggesting that anyone here makes that claim. It still has a following, alas…)