Synthetic biology, a field that aims to make biology easier to engineer, is routinely described as leading to an increase in the dual-use threat, i.e., the potential for the same scientific research to be used for peaceful purposes or misused for warfare or terrorism. Fears have been expressed that the de-skilling of biology, combined with online access to the genomic DNA sequences of pathogenic organisms and the reduction in price for DNA synthesis, will make biology increasingly accessible to people operating outside well-equipped professional research laboratories, including people with malevolent intentions. The emergence of do-it-yourself (DIY) biology communities and of the student iGEM competition has come to epitomize this supposed trend toward greater ease of access and the associated potential threat from rogue actors. In this article, we identify five myths that permeate discussions about synthetic biology and biosecurity, and argue that they embody misleading assumptions about both synthetic biology and bioterrorism. We demonstrate how these myths are challenged by more realistic understandings of the scientific research currently being conducted in both professional and DIY laboratories, and by an analysis of historical cases of bioterrorism. We show that the importance of tacit knowledge is commonly overlooked in the dominant narrative: the focus is on access to biological materials and digital information, rather than on human practices and institutional dimensions. As a result, public discourse on synthetic biology and biosecurity tends to portray speculative scenarios about the future as realities in the present or the near future, when this is not warranted. We suggest that these myths play an important role in defining synthetic biology as a promissory field of research and as an emerging technology in need of governance.