Despite evolution being the central idea in modern biology, considerable variation exists in its acceptance around the globe, and reports of anti-evolutionist and creationist movements are widespread. Educators need to re-evaluate the approaches used for teaching students about evolution in order to facilitate its understanding and acceptance. A major hurdle in understanding the concepts of evolution is that humans tend to view the world in a teleological way. Learners create obstacles to understanding the concepts of evolution by ascribing purpose or intent-driven actions to animals, processes, or inanimate objects. An indispensable learning tool in the field of evolution is the evolutionary tree, as it is a direct representation of evolutionary hypotheses. The ability to read and understand this form of representation is prerequisite to fully understanding the concepts of evolution. In this work, we present issues faced when attempting to teach students to read evolutionary trees as well as troublesome diagrammatic properties that may foster teleological thinking. Further, we present teaching practices and methods that may be used to avoid the above challenges (from diagrammatic and instructional perspectives). With this work, we aim to raise awareness among educators about the different potential teleological pitfalls in the field of teaching how to read evolutionary trees, and to present different approaches for minimizing teleological reasoning and thinking in evolution education.