Properties of non-canonical GC base pairs and their relations with mechanochemical cleavage of DNA are analyzed. A hypothesis of the involvement of the transient GC wobble base pairs both in the mechanisms of the mechanochemical cleavage of DNA and epigenetic mechanisms involving of 5-methylcytosine, is proposed. The hypothesis explains the increase in the frequency of the breaks of the sugar-phosphate backbone of DNA after cytosines, the asymmetric character of these breaks, and an increase in break frequency in CpG after cytosine methylation. As an alternative hypothesis, probable implication of GC+ Hoogsteen base pairs is considered, which now exemplify the best-studied non-canonical GC base pairs in the DNA double helix. Also see the video abstract here https://youtu.be/EUunVWL0ptw.