I have a chair like this(shown in figure). I was kneeling on the part where we sit. I just gave a sudden push to the part where we rest the back, without moving my legs. I found that the chair is moving little in the direction I applied the force. I couldn't find any reason why this chair would move forward because I am inside this system and no external force is coming from outside. When I apply the force on it , equal amount of force I am applying there on the seat in the opposite direction, so there should not be any movement.
I tried this experiment again right now. Now holding on the handles of the chair. Did the same thing. Again found the chair moving.
Where I am wrong and how does the chair move?