The biosynthesis of DNA inherently competes with RNA synthesis because it depends on the reduction of ribonucleotides (RNA precursors) to 2’-deoxyribonucleotides by ribonucleotide reductase (RNR). Hence, RNA viruses can increase viral RNA production in cells by partially blocking the synthesis of DNA, e.g. by downregulating the mammalian selenoprotein thioredoxin reductase (TR), which normally acts to sustain DNA synthesis by regenerating reduced thioredoxin, a hydrogen donor for RNR. Computational and preliminary experimental evidence supports the hypothesis that a number of pathogenic RNA viruses, including HIV-1, Ebola, Zika, some flu viruses, and SARS-CoV-2, target TR isoforms by antisense. TR knockdown would create a host antioxidant defect that could be partially rectified by increased selenium intake, or be exacerbated by selenium deficiency, contributing to viral pathogenesis. There are several non-selenium-dependent means that viruses might also exploit to slow DNA synthesis, such as targeting RNR itself, or components of the glutaredoxin system, which serves as a backup redox system for RNR. HIV-1 substantially downregulates glutathione synthesis, so it interferes with both the thioredoxin and glutaredoxin systems. Computational results suggest that, like Ebola, SARS-CoV-2 targets TR3 by antisense. TR3 is the only TR isoform that includes an N-terminal glutaredoxin domain, so antisense knockdown of TR3 may also affect both redox systems, favoring RNA synthesis. In contrast, some DNA viruses encode their own glutaredoxins, thioredoxin-like proteins and even RNR homologues – so they are doing just the opposite, favoring DNA synthesis. This is clear evidence that viruses can benefit from shifting the RNA:DNA balance to their advantage.