1) As native trees have been present from just after the last ice age, they are a essential part of our ecological make up. They will support many more fauna (and fungi) than non native. This is then magnified by the fauna that live off the directly related fauna, the fauna that live off of the indirectly related fauna etc etc
2) Native trees are optimised to our climate/conditions. This is also a weakness, if climate changes i.e. it gets hotter/drier potentially our native trees cannot cope. In this case non-native trees suited to the new climate will cope better.
3) This may just be an Arborist's point of view. Native trees sit better in our landscape. They do not disrupt the landscape. Think of a normally magnificent mature Purple Beech central to your favourite bit of woodland. OK the contrast will be stunning, but doesn't it look out of place?
4) There are varieties of native trees that have different canopy shapes (usually more upright), more flowers, less fruit etc. These will have the same benefits as native trees but may suit the planting location better.
This is not an exhaustive list!