Video narration
Why do the two electrons on one orbital get opposite arrows? Think of the orbital as a two-seat classroom bench: one electron per seat. But the arrows are not showing tiny balls physically rotating in opposite directions. Here is the key turn: spin is an intrinsic quantum property, and for an electron the spin quantum number, m_s, has only two allowed values: +1/2 and −1/2. The arrows mean those two states-up and down-not literal directions of rotation. Now connect that to the Pauli exclusion principle: electrons sharing one orbital already have the same n, l, and m_l, so they must differ in m_s. That is why the bench holds two, but only with opposite spin states. So, why opposite arrows? Because one orbital can hold two electrons only when their spin quantum numbers are +1/2 and −1/2.