Why don't electrons have the same spin even when in same orbit?
The Pauli Exclusion Principle says no two electrons can have the same quantum numbers, and there are roughly two ways to interpret this.  

First, an 'orbital' may host two electrons so long as they have opposite spins.

Second, an 'orbital' may only host one electron, but there is a second orbital that is geometrically and locationally identical which hosts an electron of the opposite spin of the first orbital.

Why?  It is written into the fabric of the universe.  That is how the math works out.  Experiments have strongly supported Quantum Mechanics.