Mongo pushing in skateboarding is when you push with your front foot as opposed to your back foot. People often criticize mongo pushing because it can be dangerous and is arguably a far less stable way of pushing. With your back foot staying on the board while you push, you could possibly press down on the tail and fall. Second, having the majority of your weight on your back foot while skating leads to rear steering which is the main cause of speed wobble. You will always be most stable by steering like a car, doing most of the steering with your front trucks, thus having the majority of your weight on your front foot while skating.
Some people do mongo push however, especially certain pros when in the switch stance. A lot of people choose to push mongo when switch because they feel more comfortable that way. At the end of the day, the way you skateboard is all preference. However, we want you to be safe while skateboarding so we do not recommend that you push mongo. You could also get called a poser if you choose to do so :)