The "affinity maturation" of the humoral immune response is driven by antigen-activated somatic hypermutation (SHM) of the genes that encode antibody variable regions and the subsequent antigenic selection of mutant clones. The molecular mechanism of SHM is yet to be completely elucidated. SHM affects cytosine-guanine (C/G) and adenine-thymine (A/T) pairs with approximately equal frequency in vivo. The proposition that error-prone DNA-dependent DNA synthesis explains A/T-targeted hypermutagenesis seems to have mainstream support within the hypermutation research community at present. A major feature of SHM in vivo is that C/G hypermutation is strand unbiased, whereas A/T hypermutation is strand biased. We show that the "DNA-based polymerase error" model of A/T-targeted hypermutagenesis does not explain this important aspect of SHM.