Stick to your guns and refuse to re-negotiate your rates. That's not being arrogant (regardless of whether it's a non-profit, or a Fortune 500 company you're doing the work for). Your rates are your rates, and if they trot out the "Johnny the neighbor's kid who'll do it for $50" line, you're better off without them as a client. I'd say they're being arrogant for trying to "discuss" the cost.