The relativity principle does NOT say that all frames are equivalent, just the inertial (unaccelerated) ones. In the twin “paradox” situation, the traveler and stay-at-home both figure that the other is ageing more slowly while their relative velocity is constant but when the traveler turns around he or she figures that the stay-at-home suddenly ages much more rapidly. The two may have different explanations in mind for the effect, but when they get back together they agree on the result.
Source: (3) Alan Cooper’s answer to How can a moving/faster observer see a ‘stationary’ clock running slower, when it doesn’t, e/specially when his really does? All the YouTube videos about the Twin Paradox say so. In what sort of universe is that possible? – Quora