In this chapter I address flaws in lineage thinking that are common in the professional, popular, and eductional literature, and which result from confusing the branching relationships between collateral relatives in the realm of systematics with the linear relationships between ancestors and descendants in the realm of evolutionary descent. The influential voices of the late Stephen Jay Gould and Robert O’Hara, who dubbed the now ubiquitous phrase ‘tree thinking’, have warned readers for decades against the sins of linear evolutionary storytelling and the use of linear evolutionary imagery. However, I argue that their impact has been deeply pernicious. The writings of Gould and O’Hara fundamentally misconstrue the relationship between the branching realm of systematics and the linear realm of evolving lineages. I close with a discussion of the problem that, in the absence of a vocabulary designed to talk about lineages, we are forced to discuss them in the taxic language of systematics. This inevitably causes problems.