You are not actually erasing possessions but every time you give up a turnover that drive can not score so it's like never having it . Also they don't need to score to make it an extra possesion, because they do in fact have extra possession because they just took yours, which is why it's likes subtracting from one and giving to the other. Think of it like an onside kick, if you make you get another possession, when you get a turnover you get another possession. Fuzzy math aside turnovers make it hard to win especially when you have an offense like ours.