The point is our freedom ends where the other person's freedom begins. So, we may plant trees in our land area only, but, if the roots go into other's lands and impact the structures thereon or the trees are such that generally lower the water table and/or trees are of the variety that branches grow into neighbour's area of land dropping lots of foliage dry twigs etc, the neighbour has every right to object.
We can plant any tree within our land area which shall occupy our land and affect us only. If you are interested in the plants, do plant small variety like Rose etc which do not grow too much and create hindrance to the neighbour.
In any case, dispute on such a simple matter with neighbour does not speak well of us. Therefore, please ensure that the matter is amicably settled.