Phylogenies are increasingly prominent across all of biology, especially as DNA sequencing makes more and more trees available. However, their utility is compromised by widespread misconceptions about what phylogenies can tell us, and improved tree thinking is crucial. The most-serious problem comes from reading trees as ladders from left to right - many biologists assume that species-poor lineages that appear early branching or basal are ancestral - we call this the primitive lineage fallacy. This mistake causes misleading inferences about changes (...) in individual characteristics and leads to misrepresentation of the evolutionary process. The problem can be rectified by considering that modern phylogenies of present-day species and genes show relationships among evolutionary cousins. Emphasizing that these are extant entities in the 21st century will help correct inferences about ancestral characteristics, and will enable us to leave behind 19th century notions about the ladder of progress driving evolution. (shrink)