Neighbour dispute...?

My Neighbour built a detached garage right up against the property line between our houses. He built it beneath a tree that is plants just on my side of the property line. He is now claiming that this tree is causing moss to grow on his garage roof shingles and that I need to cut it down. I don't want to cut it down because it's the only thing that blacks any view of his stupid garage. I understand he can trim any branches that cross the property line, but that won't solve the shade problem. Is it legit to tell him to move his damn garage, because the tree was there first!