Evolution may occur on ecological timescales, causing ecological and evolutionary effects to result in eco-evolutionary dynamics. Antiphase predator-prey dynamics are a striking example of this, and have been held up as a “smoking gun” for the presence of eco-evolutionary feedbacks. While found in both experimental and modelling studies, it is unclear when they are expected to occur. We study in detail a predator-prey model with mutual adaptation, using an extension of the Geber method to disentangle ecological and evolutionary effects on both predator and prey dynamics. We provide a predictive theory to explain what drives antiphase dynamics and when they occur. We show that antiphase cycles are only possible if the predator cannot respond rapidly or strongly to evolution of defense in prey, i.e. if evolution of offense is slow and costly. This arises from the interplay between prey biomass and trait dynamics: for antiphase cycles to occur, prey biomass and defense must cycle synchronously, resulting in prey peaks consisting of highly defended prey. This occurs when the benefits of defense strongly outweigh the costs. Conversely, if defense is costly, prey peaks consist of undefended prey, leading to classic quarter-lag cycles. This insight is key to unite previously contradictory results.