Tarnish is when the metal picks up an extra atom, mostly oxygen or another smaller atom. You cannot force the silver to release the atom without refining the metal using very reactive processes. But, with either an acid or a base you can dissolve these molecules leaving a clean surface. Baking soda is high ph with a built in abbrassive, so you're removing a fairly significant amount of metal. This works with ketchup, spit, coffee, Bon Ami, and many, many over the counter polishes. They all work, but done too often you can be left with a significat amount of the metal eaten away. I see this day in and day out with silver. Silver has a small atom, compared to gold and platinum, and it has a moderate melecular bond, which makes it prone to dissolving easily. I've seen silver urns used for coffee get holes eaten in them from today's highly acidic coffee.
Also, metal has, on a microscopic level, all these hairs or shards that will stick up, making the metal have more surface area, patina-ing faster, and leaving it with a bone white to low luster. All of these home remedies leave the metal suseptable to further faster oxidation and low polish. Brushing down the surface gently with a polishing cloth, you get a high shine, protevted surface sealed by laying all the hairs down, and more reflectove color. The polishing cloth has two layers sewn together. The light sode has an acid abrasive that will remove the moleculse. So, use the light side very gently. The darler side is designed to lay down the metal's surface. I use the acidic abrassive side on my stems, and only on metal that really needs to be cleaned. The other side is what I actually polish the metal with.
But, people really like to use these home remedies. And, if someone really wants to use them, they have my blessing. It is cool to see the metal dissolve right before your eyes. It keeps me in the repair business. Sort of like my dentist gives the kids chewing gum after cleaning their teeth. :
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