Methylation of cytosines in the DNA is central to the epigenetic code. The patterns along the DNA formed by these chemical marks instruct the cell which proteins to express and their faithful maintenance after replication are vital to the organism's life. Although Dnmt1 is the enzyme catalyzing the methylation reaction, it was found that UHRF1 (ubiquitin-like, containing PHD and RING finger domain 1) is the protein that actually recognizes hemi-methylated CpG sites. Nevertheless, the physical mechanism driving the strikingly robust distinction between hemi-methylated and unmethylated sites is not known. In this paper, we show that the large difference in the binding affinities of UHRF1 to these sites is possible not due to the presence of the methyl group itself but is a result of the accompanying changes in the distribution of the electrons around the cytosine ring. In particular, methylation reduces the dipole moment of cytosine and, as a consequence, unmethylated DNA in its unbound state in water is more stable than hemi-methylated DNA. Furthermore, the interaction energy of hemi-methylated DNA bound to UHRF1 with its surrounding is stronger than that of unmethylated DNA. Thus, the change in the electronic structure of cytosine upon methylation destabilizes the unbound state and stabilizes the bound state rendering discrimination with high fidelity possible.