Your eye finds a middle. It is rarely the middle you were asked for.
Ask someone to point at the middle of a wine bottle and they will point too high. Ask for the middle of a hammer and they will point too far from the head. The errors are consistent, and they are not carelessness.
There are at least three different middles, and the eye is not reporting the one you asked about.
The centre of the bounding box. Halfway along the object's total length, ignoring its shape entirely. Easy to find, almost never useful.
The centre of area. The point where a line divides the silhouette into two equal areas. This is what "cut it in half" usually means when the object is flat and uniform.
The centre of mass. The point where the object balances. This is what "half" means when weight is what matters, and it depends on density as well as shape.
For a rectangle of even thickness, all three land in the same place, which is why rectangles feel easy and teach you nothing.
For a wine bottle they are far apart. The bounding box centre is halfway up the glass. The centre of area sits lower, because the body is much wider than the neck. The centre of mass sits lower still and moves as you drink.
Vision estimates something close to the centre of the bounding box, then corrects slightly toward wherever the visual weight is. That correction is real but too small.
The result is a predictable bias: the eye underestimates how much a wide section outweighs a narrow one. A shape that is fat at one end and thin at the other gets halved too close to the fat end, every time, by nearly everyone.
The size of the error grows with the ratio between the two ends. On a shape that tapers gently you will be within a few percent. On a shape like a bowling pin or a light bulb you can be off by a fifth.
Two objects with identical outlines can have completely different balance points.
A hammer is the clean example. Its silhouette is mostly handle, so the centre of area sits well down the shaft. Its mass is mostly head, so the centre of mass sits close to the top. Cut a hammer at the centre of its area and one piece will weigh several times the other.
This is why "cut it in half" is an ambiguous instruction until someone says what is being halved. Halving the picture and halving the object are different tasks, and only one of them can be done by looking.
The one reliable technique is to stop looking for the middle and start comparing the two halves.
Pick a candidate line. Then ask, honestly, which side would win if the two pieces were weighed. Move the line toward the winner and ask again. Two or three iterations of that beats a single confident guess, because comparison is a much easier judgment than estimation.
It is the same reason a balance scale was invented before an accurate spring scale. Telling which of two things is heavier is easy. Saying how heavy either one is, is hard.