We consider the class of balancing algorithms for two servers. Such algorithms have appeared in a number of the early papers on this problem; they are so named because they seek to "balance" the distance travelled evenly among the servers. In this paper, we show a universal lower bound on the competitive ratio of any balancing algorithm for two servers. The lower bound is equal to (5 + $\sqrt{7}$)/2 ($\sim$ 3.82), and consequently shows that no optimal on-line algorithm for two servers can be expressed as a balancing algorithm.