Why and how does baking soda whiten a person's teeth?

Not very effective: Baking soda has no real bleaching effect on your teeth. If can be a mild abrasive for removing stain, similar to tooth paste. Some time used with hydrogen peroxide is will have a oxidizing effect on teeth and can be useful controlling gum disease and inflammation.

Baking soda teeth: The chemical structure of baking soda also makes it a mild abrasive, and that's why it's so effective for removing surface stains from your teeth. Baking soda crystals are unique in that they dissolve easily in water, whichich allows the baking soda to penetrate more deeply into the grooves of your teeth and hard-to-reach places in your mouth than some other abrasives can.

Not Recommended: Baking soda is highly abrasive and removes enamel therefore it is highly not recommended.