It's one of those flat-Earth standards that nearly every proponent of this nutty idea will throw at you at some point: "The horizon always rises to eye level no matter how high you go; on a ball the horizon would fall away and you'd have to look down."
Well, here's the problem. The horizon would also fall away on a flat Earth, just not as fast, and the difference is very, very small because the Earth is very, very big. The horizon is never at eye level unless eye level is right on the ground.
The real conceit behind the claim, though, is that trusting the evidence of your eyes had more validity than measuring it with instruments. And that's just nonsense. Humans are not precision instruments. That's why, as soon as we started making things, we started inventing better ways to measure things.
I was at an antique and consignment store today, and I ran across a micrometer. All I was thinking at the time I saw it was that it was a pretty amazing instrument. Properly-used these mechanical devices can measure the size of a small object to a precision of .005 millimeters.
Then, later in the day, a flat-Earther tweeted the same old saw about the horizon and I thought: "What hubris, to think that anyone can tell whether he is looking perfectly straight ahead or a couple of degrees downward."
There is a simple test you can perform to see how good you are at determining your eye level. Stand about 15 feet away from a wall that has a good-sized picture on it with details you can focus on. Decide which detail is at your eye level. Now, have someone measure your eye level, and then measure the distance from the floor to the detail. Or, if you don't have someone handy to measure, just walk right up to it and see how far you were off.
My 16-year-old son tried this, and he was off by more than 1.25 degrees. And this is easier than knowing where the horizon lies in relationship to your eye level, because in the case of the horizon there aren't a lot of other visual cues.
Here, a simple measuring tape has bested your eye-witness evidence. And, of course, a more precise instrument like a theodolite could determine if the horizon, from different viewing heights, really is at eye level. And in test after test, it has been shown that it does not. In an airplane, the difference is big enough that a simple theodolite app for a phone can indicate the gap between the level and the horizon.
And yet this myth persists, by people who just accept it as true without performing any intelligently-designed tests, with no effort at all to falsify their own claims.
But then, that kind of thinking is why we have flat-Earth belief in the first place.