I am a 11th/12th grade student studying orbital configurations. I have gone over this lesson and it says to always draw spin up first. However, it never says why. Is drawing down spins first incorrect?
There is no real reason about that and drawing them "down" would be exactly the same as long as you draw them always in the same direction (it needs to be consistent).
The same applies to orbital lobes which can be hollow (white) or plain black depending on their relative sign. When two molecules' orbitals interact, you just consider they have the right sign for an interaction.