The reasoning behind splitting certain pairs in blackjack, such as Aces and Eights, is to maximize potential outcomes. Splitting Aces allows players to create two hands starting with a value of 11, increasing the chances of hitting a blackjack. On the other hand, splitting Eights transforms a weak hand total of 16 into two separate chances for better outcomes, reducing the risk of busting and improving winning odds. These strategies are fundamental to basic blackjack strategy, aiming to optimize expected returns based on statistical probabilities.