Wait and See
Why is the wait-and-see approach so important for an assistant referee? Especially when you have two attackers with one being in an offside position and the other in an onside position, you want to give yourself extra seconds to raise your flag to make sure that it is indeed the offside player who plays the ball, interferes with an opponent, or gain advantage. If you raise your flag and an onside player plays the ball, your flag was premature. A premature flag could easily take away a goal.
The video below shows how important it is for an assistant referee to wait and see. If the AR had raised his flag prematurely, this goal would not have happened.