I am not a horticulturist and know very little about gardening. However, when I was a child, my Dad used to have this mango tree planted in our garden just next to our neighbour's house. For most of the day, my neighbour's house provides a bit of shade to the mango tree. We have noticed over the years that the side of the mango tree that gets more exposure to the sun, actually bears more fruits and definitely sweeter fruits as well. That's just my answer based on child hood observations.

Cheers,

RedMatter

If this fruit tree was originally bought from a nursery, it may consist of two or more varieties grafted onto a single stem. I have such a tree growing in my garden consisting of three apple varieties. Some environmental factor might then be weakening the tree, so that only one of the varieties is capable of flowering. If this is the case, a closer examination of the tree will reveal graft scars where the major branches join onto the trunk.

Because it is sick! Or you've been using herbizides on one side...

An herbicide, commonly known as a weedkiller, is a type of pesticide used to kill unwanted plants.[1] Selective herbicides kill specific targets while leaving the desired crop relatively unharmed.

You have had some pretty good answers. All the suggested causes do occur from time to time.

If the difference is varietal, there would be differences in the stems as well, but often it takes a specialist to detect this.

I doubt that herbicides are involved, but there might be some nasty material underground, affecting the roots on one side. I have a tree in my garden with its branches on one side growing at least twice as fast as on the other. We are pretty confident that the builders of the house (it is fairly new) had filled up a hollow in the ground towards one side of the tree with builders' rubble. 

The direction and intensity of shading also are important in practice.  Note also whether it is an absolute difference in flowering or not, rather than one side flowering earlier.

Hmmm... I have had a closer look at the photo. The branch without the flowers seems firstly to be of a different shape, possibly younger or of a different variety, and seems to be growing closer to a wall of a house.

Already such factors might suffice to explain the effect.