I am trying to figure out the reason why magnets are magnets. I understand that atoms become magnetic when there is a net direction of spin of electrons around the nucleus; however, I do not understand why the electrons revolving around the nucleus of the atom create a field that "start" at the north pole and "end" at the south pole. (I put the quotes because I understand that the start and end is just a way for us to show in words how test charges move in a magnetic field) please feel free to correct me on anything I am missunderstanding. Thank you.
So at the most fundamental, if you ever have two wires that are parallel and they have an electric current going through them in the same direction, they attract. This is a bit of a mystery, and we can dive in a little bit deeper by talkin about principle that unifies the magnetic force into the electrical force, called relativity—but there are limits to how far we can go in the space of one less-technical stack exchange post. So I need you to just understand that if you have two parallel wires, then when electric currents go down them in the same direction, they attract, and if currents go to down them in opposite directions, they repel.
It follows that if you twist them into a loop, creating a spinning electric current, that loop has a certain handedness around the axis. The rule is that you take your left hand, and place it on the loop so that electrons are moving from your palm to your tip of your middle finger, and then your left thumb is pointed in some direction. Coincidentally, if this loop happens to be on the surface of the Earth, it would tend to reorient so that this left thumb is oriented North, and we call that left thumb the North Pole of the magnet.
Since parallel currents attract, two rings of current would like to stick on top of each other. So north poles attract south poles, and they repel other north poles, because if the north poles point at each other, then the currents of the loops are opposite, and opposite currents repel.
What is somewhat confusing, but true, is that inside our Earth there is a magnetic core which points opposite the direction that you believe. Its magnetic north points at Earth's South Pole, and its magnetic South points at Earth's North Pole. This is why magnets want to point with their north magnetic poles pointed towards Earth's North Pole, because it is a magnetic-south pole for some big magnet.
Now this convention which one is north and south, is very arbitrary. It is arbitrary, first off, because it depends on whether you consider the proton or the electron to have positive charge, and the electricity is carried by an electric current of moving electrons, we consider them to have negative charge, so they always flow in the opposite direction of the current. And then the next arbitrary thing is called the right-hand rule, and it says that you should not use your left hand, like I told you to, but should use your right hand, but for positive current. So I told you to make the electrons go from your left palm to its fingertip, but we arbitrarily say that you should make the electric current go from your right palm to its fingertip, and since electrons carry negative charge and therefore describe negative currants, the electrons would be flowing from the your right fingertips into your right palm. What is not arbitrary is that the electrons in the core of the Earth are moving from west to east about the axis, but as long as you have the same rule for the electrons in a wire and the electrons in Earth's core, you will get the same result that magnets have a consistent way on Earth's surface that they want to point.
And once you call one of the poles of the magnet north because it points North, and one of the poles of the magnet south because it points South, then you can meaningfully say that north poles repel but a north pole attracts a south pole.
But in terms of fundamental explanation, it doesn't get easier than just saying that like currents attract and opposite currents repel, and it comes from the fact that if you were following an electron and could see the world from its perspective, the other wire would appear to have a net positive charge, and opposite charges attract. Roughly speaking, that is because in the reference frame where the wire is at rest, we would say that the positive and negative charges are perfectly balanced, so the wire has no charge. But when you move, you simultaneously cancel out a lorentz contraction of the moving electrons, and create a lorentz contraction of the stationary atoms: this causes the electrons to appear less dense, and the positive nuclei to appear more dense, so there is a change in the apparent charge density on the other wire.