Bicyclists have places to go and those places are often, disproportionately even, on the "main road". Asking cyclists to bike at least two blocks out of their way is not reasonable. Also often those side roads have uncontrolled crossings of other busy roads which makes traversing them practically impossible.

The real question is why a car, which can effortlessly stop, go, and turn without any exertion whatsoever on the part of the driver, is permitted on the shortest route. Since it's so easy for a driver to detour to a side road, the main roads should be reserved for bicyclists and pedestrians exclusively.