In electrolysis of aqueous solutions, I can loosely explain what happens at the cathode in terms of reactivity - any metal more reactive than hydrogen stays in solution, effectively because they're more attracted to water molecules. I could also explain this in terms of redox potential if I had to (I'm teaching this at GCSE level right now - to 16-year-olds - and we don't bring in redox potential or the electrochemical series until later).
But what happens at the anode is currently puzzling to me. We're told that the only anions which get oxidised in preference to hydroxide are the halides, but I can't explain that in terms of reactivity, and so far I'm not sure how to explain it in terms of standard reduction potential, either.
So - why the halides? And are they really the only anions oxidised in preference to hydroxide?