Just speaking from my own perspective...
I had a very bad experience with a dog when I was a young girl that has left me with a general fear of all dogs, no matter how big or small, leash or not.
When I'm at a park or outside and an owner doesn't have their dog on a leash, I literally panic. I start to sweat, my heart starts beating super fast, and my instinct is to get as far away from it as possible. Even recently, a dog charged me while I was out running one night and the situation left me in tears.
If your neighbor is anything like me, the encounter probably scared the shit out of him, as it would have scared me. It wouldn't matter if the dog was a weiner dog or a pit bull. For me, a dog is a dog and I don't want to see any of them. You would be amazed at how many dog owners there are who think everyone will or should love their dog.
Even now, you are berating him on a message board for his reaction. I think his reaction was perfectly normal and justified.
He will calm down (maybe he already has) but I think you should go over there and acknowledge that you were in the wrong here and you are profusely sorry. I'm guessing he'll accept your apology and that will be the end of it.

Sorry for the long post. Dog stories touch a nerve with me.