The reason the horizon appears at eye level regardless of our altitude is because the Earth is very large compared to our size, so the curvature is not immediately noticeable to the naked eye.
When we are standing on the Earth's surface, the horizon appears to be at eye level due to the curvature of the Earth. However, as we ascend to higher altitudes, such as in an airplane or on a mountaintop, the horizon remains at eye level because our line of sight extends further, compensating for the curvature of the Earth.
To better understand this concept, imagine standing on a vast, flat plane. As you look out into the distance, the ground appears to rise to meet your eye level, forming a horizontal line or the apparent horizon. Now, if you were to ascend to a higher position, the horizon would still appear at eye level because your line of sight extends farther, following the curvature of the Earth. The Earth's surface curves away from you, but the distance between you and the horizon increases proportionally, making it appear flat.
However, it's important to note that if you were to observe the Earth's curvature from a much higher altitude, such as from space, it would become more apparent. Astronauts in orbit or viewing the Earth from spacecraft can indeed perceive the Earth's curvature due to their significantly greater distance from the surface.
In summary, the curvature of the Earth is not immediately noticeable to the naked eye at typical viewing heights due to the Earth's large size relative to our scale. The horizon appears at eye level because our line of sight extends further as we ascend, compensating for the Earth's curvature.