Genomes exhibit diverse patterns of species-specific GC content, GC and AT skews, codon bias, and mutation bias. Despite intensive investigations and the rapid accumulation of sequence data, the causes of these a priori different genome biases have not been agreed on and seem multifactorial and idiosyncratic. We show that these biases can arise generically from an instability of the coevolutionary dynamics between genome composition and resource allocation for translation, transcription, and replication. Thus, we offer a unifying framework for understanding and analyzing different genome biases. We develop a test of multistability of nucleotide composition of completely sequenced genomes and reveal a bistability for Borrelia burgdorferi, a genome with pronounced replication-related biases. These results indicate that evolution generates rhetoric, it improves the efficiency of the genome's communication with the cell without modifying the message, and this leads to bias.