When designed deliberately, data visualizations can become powerful persuasive tools, influencing viewers' opinions, values, and actions. While researchers have begun studying this issue (e.g., to evaluate the effects of persuasive visualization), we argue that a fundamental mechanism of persuasion resides in rhetorical construction, a perspective inadequately addressed in current visualization research. To fill this gap, we present a focused analysis of octopus maps, a visual genre that has maintained persuasive power across centuries and achieved significant social impact. Employing rhetorical schema theory, we collected and analyzed 90 octopus maps spanning from the 19th century to contemporary times. We closely examined how octopus maps implement their persuasive intents and constructed a design space that reveals how visual metaphors are strategically constructed and what common rhetorical strategies are applied to components such as maps, octopus imagery, and text. Through the above analysis, we also uncover a set of interesting findings. For instance, contrary to the common perception that octopus maps are primarily a historical phenomenon, our research shows that they remain a lively design convention in today's digital age. Additionally, while most octopus maps stem from Western discourse that views the octopus as an evil symbol, some designs offer alternative interpretations, highlighting the dynamic nature of rhetoric across different sociocultural settings. Lastly, drawing from the lessons provided by octopus maps, we discuss the associated ethical concerns of persuasive visualization.