Understanding how complex traits, such as epithelia, nervous systems, muscles, or guts, originated depends on a well-supported hypothesis about the phylogenetic relationships among major animal lineages. Traditionally, sponges (Porifera) have been interpreted as the sister group to the remaining animals, a hypothesis consistent with the conventional view that the last common animal ancestor was relatively simple and more complex body plans arose later in evolution. However, this premise has recently been challenged by analyses of the genomes of comb jellies (Ctenophora), which, instead, found ctenophores as the sister group to the remaining animals (the "Ctenophora-sister" hypothesis). Because ctenophores are morphologically complex predators with true epithelia, nervous systems, muscles, and guts, this scenario implies these traits were either present in the last common ancestor of all animals and were lost secondarily in sponges and placozoans (Trichoplax) or, alternatively, evolved convergently in comb jellies. Here, we analyze representative datasets from recent studies supporting Ctenophora-sister, including genome-scale alignments of concatenated protein sequences, as well as a genomic gene content dataset. We found no support for Ctenophora-sister and conclude it is an artifact resulting from inadequate methodology, especially the use of simplistic evolutionary models and inappropriate choice of species to root the metazoan tree. Our results reinforce a traditional scenario for the evolution of complexity in animals, and indicate that inferences about the evolution of Metazoa based on the Ctenophora-sister hypothesis are not supported by the currently available data.