I must admit I'm terrible at physics so I don't fully grasp it, but seems like it's because the solar system formed out of a spinning ball of gas and over time the spin caused it to flatten out (like a pizza dough, I guess?).

https://science.psu.edu/science-journal/winter-2021/FlatSolarSystems

As for why atoms aren't similarly flat, it seems to be because at that small scale the gravity is a negligible factor compared to the other forces, such as electromagnetism. The electrons repulse each other.

https://www.quora.com/Our-solar-system-spins-on-a-flat-plane-so-do-atoms-also-do-this