Vigorous cardio and strength training puts stress on your muscles. Rest days give your body the chance to catch up on all the little repair jobs and are when improvements to your muscles and fitness happen. If you don't rest, your muscles never get stronger.
Rest days ultimately help your longer term performance, and reduce the risk of injury (which can derail your exercise plans a lot more than a single rest day).
A rest day doesn't mean you have to do nothing. Something like a 20 minute walk can help keep you in the groove of regular exercise, without really taxing your body.
The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.
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