Because unless you are taking a picture of a subject which has a face exactly parallel to the focal plane there are going to be converging lines everywhere and those converging line are not good for camera orientation.
Let's make a very obvious example.
You are in front of a relatively tall building. You have a small format camera. Let's make it short and decide that you are going to point the camera up in order to have the building enter the frame.
As is universal experience, all the lines which in the buildings are parallel in your frame will be converging. The lines which start from the same plane (such as those formed by the windows of the fašade) will converge to a vanishing point.
Now imagine your camera is not perfectly horizontal, and imagine the focal plane is exactly parallel to the plane of the fašade.
If the camera is bent "to the right", the vanishing point will fall on the left part of the frame.
If the camera is bent "to the left", the vanishing point will fall on the right part of the frame.
When the camera is exactly horizontal, the vanishing point will fall exactly on the middle of the frame, i.e. when the vanishing point falls along a line in the middle of the frame, the camera is exactly horizontal.
Now visualise this steel and glass building with plenty of vertical lines. When the central line (central in your frame, it doesn't matter if it is in the middle of the building fašade) is vertical, your camera will be levelled.
First case, camera parallel to fašade:
The subject will "level your camera" as the vertical line which is in the centre of the frame will be the line which, if vertical, will make the frame exactly horizontal. But in this case, in fact, all lines could be used as a valid gauge. The real interest arises when the fašade is NOT parallel to the focal plane.
In this case, your camera is levelled when, and only when, a line which is vertical in reality is also vertical in the CENTRE of your viewfinder.
Examples of camera not parallel to fašade:
The same rule applies. If the imaginary (or real) line in the centre of your frame, which is "vertical" in your frame, corresponds to a line of the fašade (which is vertical in reality, that is) the camera MUST be exactly horizontal.
PS The building is the ENI building in the EUR district of Rome.
So if I follow this advice, I will get verticals and horizontals parallel to my frame edges. Is that correct?
The rule is: your camera is horizontal if an existing line which is vertical in nature coincides with a vertical line in the centre of your viewfinder. Edges must be disregarded completely. Trying to align anything with the edges of the viewfinder is a sure way to have a tilted horizon.
Aligning lines to the frame edge is the typical mistake people make as it is in many introductory books to photography. That doesn't work. In the first ENI building example in my previous post it would work, but in the second and third example it would not. The centre line always works.
Thank you, I think I now understand.
To vertical lines on the subject... maybe, maybe not, depending on where the feature is and whether the camera is level.
A vertical line through the center of the viewfinder will always align with a centered subject feature
if the camera is level, regardless of camera tilt.
If you tilt the camera up, building edges away from the image center will converge toward the top.
Also, some lenses may introduce distortion near the edges.
An off-center vertical is actually better because it allows you to judge both tilt (right or left) and pitch (forward or back). A vertical dead center can only help with tilt.
Get one off-center vertical right and all the rest of the verticals will fall in line too.
Going farther, if you get one off-center vertical and one off-center horizontal composed "squarely" in the frame all the rest will follow. At that point only the lines leading away from the camera will converge.
While it is possible to use these concepts on any camera, fixed lenses, that can't be moved left, right, up, or down, force significant compromises in composition and camera placement, generally leading to serious cropping.
Also lens distortion, barrel or pincushion, complicates things too.