Please note that the question is "Why", not "How".
For sure I'm getting this wrong, but I'm stuck and I don't know why! If a reverse thrust is applied during an aircraft landing wouldn't the total amount of work necessary to pull the air inside the turbine (hence pushing the aircraft forward) be canceled by the amount of work used to push the air forward (i.e. pushing the aircraft backwards)? I mean, why does it work? Why does the net work push the aircraft backwards and help to stop the plane?