Am I responsible for trimming a tree that is on my property but extends my niebors fence??
You are responsible, it is your property and the tree even reflects the value of your property. Telling you to cut the tree extending onto his property is a nice gesture. My neighbor just cut one of my trees overhanging their property and they butchered the tree. I told my neighbor to contact me and I would take care of their concerns with my trees immediately. Go and look after your tree, don’t let someone mess it up for you.