Rest days also prevent burnout. When we refuse to take one it would be like refusing to stop and get gas when our car is on empty. Much like a car we will eventually run out of fuel which leaves our body with no choice but to shut down without any energy. This turns your one-two days of rest into a week or two. In the end, it leaves you out of the gym even longer than if you scheduled a rest day once or twice a week to begin with.
Much like when we sleep, our bodies need rest days so our muscles get the time they need to grow and repair. If we don't take the time to let them rest we are hindering their growth and we will stay at a stand still seeing less progress. If you want to see progress take rest days.
As athletes we not only go through extreme physical challenges but our minds go through mental stress as well. Rest days give us time to refocus and re-plan. Without them we become cranky and stressed out. Rest days create happier athletes in the end.