Unfortunately, just like current flowing from the positive to negative direction, and the potential between the terminals of a battery being called electromotive “force”, we are stuck with the name “spin” due to historical reasons.
To understand ineptitude of some of the brightest minds that have graced this planet when it comes to naming things, we should understand what spin even is and how it was discovered.
Classical mechanics says that whenever a charged particle moves, it creates a magnetic field. When you make a charged particle move around in a loop, it creates a magnetic field which looks identical to the magnetic field created by a bar magnet. Since this was something that was known even before quantum mechanics, it was embedded in all the equations of quantum mechanics. Later on, however, some experiments showed that charged particles must have some other source of magnetism (in addition to the magnetic field produced when they moved). This source of magnetism was called spin.
One of the experiments that showed this was the Stern–Gerlach experiment. If you place a small bar magnet in a Stern-Gerlach apparatus, then it would tell you the orientation of the magnet (only in the direction of the set-up). It does this by exerting a force in the direction the magnet is pointing most in. In some orientations, the magnet does not experience any force at all. So if we take a bunch of magnets in random orientations, we expect to see them go through the apparatus in a pretty smooth distribution: some would go up, some down, some won’t move and other would only travel half the distance. If we ditched the magnets, and threw in electrons (which are not doing any loops) in the apparatus, something really weird happens. Not only do all the electrons experience a force, they do not do so in a smooth fashion. Half go up all the way and half go down all the way. If the electrons really were little tiny magnets, then they should be randomly oriented in space, which these electrons clearly are not.
The Stern–Gerlach apparatus can be used to measure “how magnetic” something is in any direction. If we turn the apparatus on the side, then the machine would measure how left/ right the magnets are pointing in space. But doing so with electrons, we get the exact same result, that is: half the electrons go left and half go right.
Sooooo, what’s happening here? The electrons are not doing little loops, but still they’re behaving as though they are. The people who discovered this thought, maybe the electrons are spinning on their own axis, just like the earth spins on its axis. This should have worked because bits of charge on the electron would move in a circle and create the magnetic field. Thus this property was dubbed spin. But, later calculations showed that the electrons would have to spin faster than the speed of light to achieve the kind of magnetism that was observed. But, that obviously cannot happen. So the electron clearly is not spinning. These days, when we are not talking about electrons as waves, we talk about them as infinitely small points, and those most certainly can’t spin.
What is spin, you ask? Spin is the property of particles that make them act like magnets, it has nothing to do with the particle actually spinning. Nothing more, nothing less. You would have better luck trying to explain to ants how to use rice cookers than you would ave looking for an accurate classical analogy of spin, it just does not exist.