Cyclical time stands in direct structural tension with any tradition built around a single, unrepeatable narrative arc, a unique creation, a unique fall, a unique incarnation or revelation, and a single final judgment or end of days, which is precisely the shape of mainstream Christian, Jewish, and Islamic salvation history, and this is not a minor disagreement about calendars but a disagreement about whether any event can be genuinely unrepeatable and therefore uniquely significant in the way those traditions require their central events to be.
Friedrich Nietzsche's philosophical thought experiment of eternal recurrence, the idea that one's exact life might repeat identically an infinite number of times, is a modern secular descendant of the same structural idea, used by Nietzsche not as literal cosmology so much as an ethical test of whether one could affirm one's own life fully enough to will its endless repetition.
Within traditions that hold cyclical time, the position raises its own internal tension worth naming honestly: if the same essential pattern always recurs, what, if anything, makes any particular cycle's choices matter, a question Hindu and Buddhist traditions answer differently, generally by locating what matters not in altering the cosmic cycle itself, which no individual action can do, but in an individual's own progress toward liberation from the cycle altogether.