Indigo Airlines — Not allowed to board the flight!

Website:

book.goindigo.in

Even-though we called up @ 4 PM on Friday, 12/Feb/2016 to indigo customer care requesting them to forward our message to the Kempegowda International Airport, Bangalore that "We got stuck in a very bad traffic, we will be reaching airport in between 4:30 PM-4:45 PM. So please allow us to board our flight",
WE WEREN'T ALLOWED TO BOARD OUR FLIGHT.

We were at check-in Baggage counter @ 4:40 PM & web check-in was already done.

Please reply my below queries:

I was told by the supervisor at the airport that "We have received your request but we can't allow you!", now what is the difference between not making a call & making a call to Indigo customer care and requesting them?

Since web check-In was already done, other airport formalities should have been completed in 5-10 min, then why we were not allowed to board our flight?

In worst case, Indigo could have done the following:

By Allowing us to board the flight & luggage could have been sent to Kolkata with the next immediate flight.

Emergency gates could have been used to board the flight.

Since we were not allowed to board the flight, It's a financial loss to me apart from missing an important meeting in Kolkata.

It would be a favor from Indigo if:

The fare gets refunded or

Gets adjusted in my future trips to Kolkata.

Request you to do the needful so that a Indigo frequent flyer like me keep faith & be loyal to the airline.

PS: As per my interaction with Army people at the airport, Indigo could have made it possible to me!


Thanks & Regards,
Mayank