I hope you realize that you are the bad guy in this scenario.
You have the right to trim limbs that hang over your property, as long as it doesn't damage the health of the tree. That's it. You can't kill part of a tree, just like you can't kill part of a person or part of a cow or whatever else.
Your neighbor is not crazy for wanting the tree to remain healthy. Trees are a good thing for both the environment and for mental health and are important for providing shade in a warming world. Their leaf litter is also important for insects and birds.
Getting so worked up about some leaves that you want to kill somebody else's clearly beloved tree suggests that you are being unreasonable. Invest in a leaf blower or hire someone to deal with the leaves if it's such a big deal to you. Or, better yet, leave them so they can help the local environment.