Popper’s falsificationism is frequently referred to as a general normative reference system in phylogenetics. Referring to falsificationism, phylogeneticists have made four central claims, including that frequency probabilities (1) cannot be used for inferring degrees of corroboration and (2) cannot be used in phylogenetics because phylogeny is a unique process, (3) likelihood methods represent verificationist approaches, and (4) the congruence test is a Popperian test. However, these claims are inconsistent with Popper’s theory. Moreover, phylogeneticists have proposed four strategies for dealing with the unfalsifiability of cladograms, including (1) interpreting re-interpretations of putative synapomorphy as homoplasy as Popperian ad hoc manoeuvres, (2) decoupling corroboration from falsification, (3) interpreting the tree with the highest likelihood as the most corroborated tree, and (4) interpreting tree hypotheses as Popperian probabilistic hypotheses that do not have to be falsifiable. These strategies are also inconsistent with Popper’s theory. Four fundamental problems and a problem with Popper’s formula for measuring degree of corroboration demonstrate that Popper’s theory does not live up to its own claims. Moreover, neither historical nor experimental sciences can be conducted in a way that is consistent with the principles of falsificationism. Therefore, phylogeneticists should stop referring to falsificationism when defending a specific methodological position.