degenreate states

[anilrapire]

would someone mind explaining why, in general, degenerate (quantum) states are not orthogonal?

[vanesch]

Degenerate states form a whole subspace. The linear superposition of two degenerate states is again a state with the same eigenvalue. So your question is equivalent to:
can someone explain me why all vectors aren't orthogonal ?

However, it is always possible to choose an orthogonal basis in this subspace, and those eigenvectors ARE orthogonal.

cheers,
Patrick.