Well, suppose that isn’t the case. This means that Black has a strategy that’s guaranteed to win no matter what White plays. But imagine that, on his first pair of moves, White moves a knight out onto the board and then returns it to its home square. Now Black finds himself in White’s shoes: All the pieces are in their original positions and it’s his turn to move. Our hypothesis says that anyone in these circumstances is sure to lose, but it also says that Black is sure to win. This is a contradiction, so the hypothesis must be wrong: It can’t be the case that White is sure to lose. Hence he must be able to achieve at least a draw.
From Svetoslav Savchev, Mathematical Miniatures, 2003.