Well…this isn’t quite true. There is a preferred line dividing the earth into two hemispheres - the equator. The earth’s axis of rotation can be determined from observation of the stars, and it can be argued that it’s natural to create Hemisphere A and Hemisphere B such that the a pole is in the center of each.
Once that’s done, the question of just how to orient the globe comes up. I’d suggest that the simplest display is to just put a stick on a stand, vertically, and impale a globe (through the poles) upon it for display. It sits nicely on a table, is pretty to look at, and spins on the same axis as the actual planet.
OK, well, which pole do I put on top? If I’m a European map- and globe-maker, I figure it would be more popular if my region (Europe) is easily visible when my globe is displayed on a table. Clearly, the best choice here is to put the hemisphere containing Europe “on top”, rather than on the bottom where people would have to crouch down to see the interesting stuff, while the less relevant stuff is on top and clearly visible.
Nowadays, many globes are made with the axis of rotation 23.5[sup]o[/sup] off of vertical, to match the earth’s actual tilt relative to the ecliptic. This strikes me as a fairly simple “next step in display accuracy” from the vertical polar axis described above.
It is certainly true that one can take any half of a sphere and label it a hemisphere. However, two hemispheres fall out naturally, and the one of most import to the people doing the map-making gets placed on top.
The preceding was mostly half-informed speculation, rather than authoritative knowledge. I think it more or less echoes what many others have been saying, but hopefully it addresses some of the points you raised, Whiskas.