The LAST act decides the Beginning
There have been several theories about the timing of Chandrayaan 2 Launch. From Neil Armstrong anniversary to 15th August celebrations in India.
But the real reason is as follows.
The Lander and the rover have to land at the specified location and .... The Location should be well illuminated and so the whole mission timing is decided with that goal.
First, the Physicist have decided the location ( high plain between craters Manzinus C and Simpelius N, at a latitude of about 70° south ).
Here is an attempt to map the site and its illumination conditions.
Image below shows the Vikram Lander's Planned position on Moon.
Left is the general view and Right side shows the same situation when viewed from the South of Moon.
Next we try to map when this location starts getting sunlight and upto what time.
On 5th Sept 2019 the the Landing site starts getting illuminated as shown in image below.
( Full disc of Moon view on Left and details on Right )
The Locations remains illuminated upto 19th Sept 2019.