Question

Why are `pi` orbitals doubly-degenerate?

Answer 1

Because they formed from the equivalent sidelong interactions of `p_x` and `p_y` orbitals, which, aside from their entire orientations, are the same orbitals. As a result, all `pi` interactions are doubly-degenerate.

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There is no difference, in principle, between the `p_x-p_x` atomic orbital overlap and the `p_y-p_y` atomic orbital overlap other than their relative entire orientations.

In fact, if you envision using your right hand to take the `pi_(2px)` molecular orbital and rotate it `90^@` counterclockwise about the `z` axis, you get exactly the `pi_(2py)` molecular orbital.

So, they are the same energy molecular orbitals.