Maybe this is too mild a solution for Brooklyn but there are a few things noted
in this exchange. Two people are not angry with each other over a tree. I have
moved ninteen times in my adult life and can attest to the fact that it is
always better to remain friendly with the adjacent neighbor. If he is new, you
can used to him.

Second a maple is a junk tree in city gardens. A silver maple is fast growing
and along with Norway maples is the scourge of city backyards. They all but
make gardening impossible under the spread of the tree. They are planted
because they grow fast and because they are usually free, seedlings being
everytwhere.

Third erecting a fence with a tree in the path is not difficult. Any fence
contractor can contrive ways to use the tree as part of the fence. This is
suggested in an earlier post though does not seem to be a favored solution. I
would do this instantly and no lawyers will be needed. If the current fence
contractor cannot do the job, find another who can. Also the tree, most maples
are guilty here, can be trimmed up high and have the branches thinned. Both
parties would be happier.

Lastly, the part about whether the neighbor would need a fence is his decision.
Fences and walls are part of property joining in all part of this world. Only
in America and mostly in suburbs is the subject of a fence a social and
cultural issue. Some HOA's and many suburban towns have ordinances fences.
The fence is often the structure that makes a good partnership with neighbors.
He may be doing you a favor.

Been There