The backtracking method assumes that once the first player made his first move, then the second player can't win by iterating all the possibilities.

However, what if the second player could win when the first player made a sub-optimal move after his first move? In other words, the first player could guarantee a win only when every move he made is the best. Otherwise, he may lose to the second player. Then apparently, backtracking can't guarantee the best move.