Common courtesy id say.Plus can you be sure you only pasint your side without it running onto theirs?Then it will look messy.Best if you both paint each side same colour .
Always better to be friendly with your neighbour and avoid conflict at all costs- why risk falling out or creating a resentment which is bound to surface sooner or later. Life is hard enough without ill feeling building into conflict.
ASK permission ! It will set you on good footing with your neighbour- You never know when you may need his co-operation for something else quite unrelated to painting a fence.....!