Why are electrons paired in orbits?

Quantum chemistry (quantum physics) tells us that each orbital can hold two electrons. The Pauli Exclusion Principle tells us that no two electrons in the same atom can have the same four quantum numbers; therefore, these two electrons may have the same n,l, and ml so they may NOT have the same ms. Thus we write one with ms = +1/2 and the other electrons with ms = -1/2.