Ultimately, he doesn't own the road and you have no obligation to comply to his request. Take an airhorn with you in case the dog does break the barrier. Use it on the other dog as well. They are a directional sound, so there isn't any harm to you and shouldn't your dog. He is responsible for his dog, not you. Just as you are responsible for yours. While I understand you might want to play nice, you've done nothing and are under no obligation.
I'm looking at it from law perspective. There are dog laws in the county as well. Find out what they are for your area.