When galaxies are younger, besides the dark matter, they are mostly gas and plasma. This gas clumps in a center so a lot of mass end up there, perhaps as quasars or primordial supermassive stars. This means there is a lot of gravity in the center.
Then the rest of the gas accelerates toward it but because of the gravity well a lot of it end up in orbit around the center. The bulk of the orbiting matter makes the whole system a rotating body. This means there becomes a desired plane of rotation, as the system now acts like a giant magnet.
When this rotating gas goes on to form stars it already is in orbit around the center so this disc shape hangs around.
Another reason is because any rogue orbits at other angles are more likely to collide, while the ones on the plane of rotation are not. So it results in a lot fewer unconventional orbits than not.
Imagine one of those coin-spinner cone things. The charity ones where you put a coin in, it spins round and round the vortex, then falls through the middle.
Now imagine you chuck in like 30 coins at random. Some are going clockwise (maybe 18), some anticlockwise (12). It’s likely that some of the coins going in opposite directions will collide. When this happens, they’ll pretty much fall in to the middle right away. But there are more clockwise coins. So if they all try and cancel out, you’ll be left with 6 going clockwise.
Galaxies are full of pockets of stuff. This stuff forms planets and stars and comets and asteroids etc. It’s going in all sorts of different directions at different speeds and distances. But if two things going on different directions or even at different angles collide, then they’ll sort of cancel each other out a bit. In reality, they’ll tend to go together in a direction somewhere between each of their directions. Eventually, stuff all cancels out until everything is going in a disk in the one direction. This is pretty much how spiral galaxies are formed. It’s also, on a smaller scale, why all the planets in the solar system go in roughly a disk (the ecliptic plane) in one direction.
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