i think he wants to be able to get vehicles through it or large items....are your gates much smaller? or is this a matter of a few inches and hes being awkward?
if the original walkway was 4ft and you have halved it, i can understand his annoyance, and id have expected you to change like for like - and given that its not only your walkway, his feelings should have been considered too
you could tell him hes free to put in a 4ft gate himself if he likes - until then yours stays.
you owe him nothing for the letters, they were his own choice.