An important class of modern channel codes is the capacity-achieving sequences of low-density parity-check block codes. Such sequences are usually designed for the binary erasure channel and are decoded by iterative message-passing algorithms. In this paper we investigate the universality of such sequences. We show that many existing capacity-achieving sequences designed for the binary erasure channel do not achieve the same capacity of many other binary-input memoryless output-symmetric channels under belief propagation decoding.