Lets assume the Earth is flat. If you took a telescope and instead of pointing it at the sky, you changed the direction to be parallel with the Earth's surface, how come you can't see a building in Tokyo, Japan when you're in San Diego, California?
You are assuming that the horizon is located an infinite distance away. It's not.
If the horizon were located an infinite distance away that would mean that a distant ship on top of the ocean horizon would be an infinite distance away. It's not.
Hence, we see that the distance to the horizon is finite. As an analogy:
An ant has a horizon located a few inches away.
A mouse has a horizon located about six feet away.
A human has a horizon located about thirty miles away.
An eagle has a horizon located over a hundred miles away.
Ergo as we increase altitude we are increasing our vantage point. The horizon is finite, changing with our altitude. Thus, the higher we go, the farther we can see and detect.
In macro photography there is a limit to the horizon. It is usually on the range of feet depending on the height of the camera from the ground. Hence, sufficient proof that the distance to the horizon is finite, tied to the altitude of the observer.