Why don't planes use Reverse Thrust to Push Back?

What is Reverse Thrust?

Reverse thrust is thrust projected in the opposite direction to normal and is used to decelerate an aircraft after landing, in the event of a rejected take off or in some cases in flight. When an aircraft comes into land, it is still moving fast along the runway. To reduce the aircraft speed, the engines can be set to reverse thrust mode. Then the flight speed going down. Aircrafts can use this functionality at any time but normally only slow down on the runway after landing. You can get an idea the process of reverse thrust and forward thrust from the above picture.

Reverse Thrust and Forward Thrust 

Aircraft Reverse Thrust

Why using reverse thrust at the gate isn't a good idea?

There are many reasons why it’s not a great idea to use reverse thrust at the gate and why many aircraft today are banned from doing so. It is completely possible to do, but that's not the best idea. Because the air blast around the aircraft will stir debris that can either damage the gate, the airport, terminal or anyone near the plane.

The power back operation uses a lot of fuel and is very loud, disturbing passengers and those watching from the airport. Lastly, pilots in the aircraft can’t see behind them (there isn’t a rearview mirror) thus, they would need a spotter on the ground anyway, negating the point of doing a movement without any help. The upside is a few minutes and dollars saved, but the downside could be millions in damage and a grounded aircraft.