Question about spin magnetic quantum number

[Bipolarity]

Not really a homework problem, just a question on the Pauli exclusion principle.
I understand that each electron has two different spins, characterized by the possible values of the spin magnetic quantum number.

However, I do not understand why it is necessary that in each orbital the two electrons NECESSARILY have to have opposite spin. Why is it not possible that both electrons in the orbital have the same spin?

 

[G01]

Where are you at in your physics studies? Undergrad? Junior? Sophomore.

The Pauli exclusion principle is a fairly deep topic, and a full explanation will require studying quantum mechanics at at least a Junior undergraduate level. If you want to know why spin 1/2 particles are fermions, then that will require quantum field theory. Thus, a bit about your physics background will help me give you an answer you are equipped to follow.