If a surface can be only be scratched by a harder material then why finger rings wear out after few years? A surface can only be scratched by a harder material. But we see so many examples where this is not true.

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*Stone floor becomes smooth even if pedestrians walk barefoot. How can human skin be harder than stone?


*Metal rings like gold, silver and brass become smooth after being continuously worn.


*St Peter's foot at Peter's Basilica in  Rome worn out due to people touching it for years.

Is it because of chemical reaction with water, sweat etc. eating away the metal? Or can a surface be scratched very slightly even by a softer material?
 A: In particular in the case of people walking barefoot:  there will always be dust particles that are stuck to the callous of the foot. Sometimes these dust particle will be half embedded in the callous, so that they don't come off when the foot is washed. Those dust particles act as an abrasive.
That is my hypothesis for stone floor being eroded over time by barefoot people.
Actually, in the case of people on shoes I think the same hypothesis is the best contenter. The soles of the shoes are a softer material than the stone, but there will always be dust particles stuck to the soles of the shoes.
Gold and silver are not wear-resistent. Silverware scratches easily, but polishing it often is not a good idea; effectively you are grinding away the object.

The wear of St Peter's foot is impressive.
I don't know enough chemistry to guess whether there is also chemical wear. That would be an interesting question to submit on a chemistry forum.
A: A partial answer to this broad question: asperities (i.e., ridges or narrow protrusions), even in a hard/strong material, can be deformed or broken off even by a soft or compliant material if the load from the latter exceeds the strength of the former. This produces a smoothing effect, with the spatial scale depending on the relative strength of the target material. Then, it takes only one encounter with a harder object to scrape or scratch up more asperities. Alternatively, chemical weathering can produce porosity, which also weakens the target material in a similar manner to a raised asperity (namely, substantially reduced cross-sectional area).
A: There are three major items you're missing:
A soft surface can be contaminated with hard grains
Other answers have touched on this already, but it's worth repeating here. If I'm walking up a stone staircase barefoot, I have to work very hard to make sure that the only material in contact with the stone is my skin. Almost certainly my feet will pick up grains of varying size and hardness from the soil and the rest of the environment. The action of walking will move those grains around on the stone's surface, like a low-quality polishing cloth, selectively breaking off sharp protrusions — the fragments of which become fresh polishing grains.
Even for a hands-only artifact like St. Peter's foot: suppose I'm the last person to touch it for the day, and my hands are sweaty. When the water from my sweat has evaporated, there will be a rime of salt crystals left behind, to be unwittingly smeared by the next person to touch that spot.
A soft surface can still damage a hard surface

A surface can only be scratched by a harder material.

This is an approximate statement, not an exact law.
Suppose I have a mass which is suspended between two springs of equal stiffness:
--((((((-- [mass] --((((((--

(I don't seem to have a good "coil" character on my ASCII keyboard.)  If I push the two ends of this apparatus together, because the springs have the same stiffness, they'll compress the same amount.  However, suppose that I stiffen the left side by adding some more springs in parallel:
--((((((-- [    ]
--((((((-- [mass] --((((((--
--((((((-- [    ]

Now, if you compress the sides together, the mass is going to move until the force from the left and the force from the right are the same.  But since we have more springs on the left, that side only needs to compress a third as much as the other. If the stiffness on either side is asymmetric, compression will push the mass towards the softer side.  And if the stiffness is strongly asymmetric, it may be a useful approximation to say that "all" of the deformation is on the squashier side.  But a useful approximation is still an approximation.
For "scratching" we are interested in plastic deformations, not in elastic deformations. But the same sort of rules apply for the plastic deformations that are the basis of the classic Mohs hardness test:

Frequently, materials that are lower on the Mohs scale can create microscopic, non-elastic dislocations on materials that have a higher Mohs number. While these microscopic dislocations are permanent and sometimes detrimental to the harder material's structural integrity, they are not considered "scratches" for the determination of a Mohs scale number.

Skin, unlike stone, is subject to homeostasis
Here's an experiment you can probably do right now. Grab a pencil and make a mark on some scrap of paper.  Then wet your thumb and use it to "erase" the mark you've just made.  This works ... kind of.  It's much, much less efficient than the rubber eraser on the back of the pencil.  You're also much more likely to end up tearing a hole in the paper with a wet thumb than you are with a rubber eraser.  And if you actually try it, you'll realize pretty quickly that, if you kept at it for long, you could give yourself an unpleasant abrasion injury, rubbing away the skin on your thumb nearly as much as rubbing away the fiber layers on the paper.
But, suppose you rub on a piece of paper until the paper is torn and your thumb is abraded.  Put it away for a week and come back.  The paper will still be torn, but your thumb will be intact again.
In the case of the statue in Rome, it has been an object of pilgrimage for centuries; many of the people who have touched it have produced entirely new pilgrims, their children, to return and touch it again.  The statue has had no such advantage.
Fermi estimation: how much of the statue is removed by one touch?
Let's do an order-of-magnitude estimate.
Suppose the foot of the statue has been shortened by one centimeter from its original size.  (One millimeter is too short; one decimeter is too long.)
How many people touch the statue in a year?  A million seems high: that would be two per minute, round the clock.  Call it 100,000 touches per year.
How long has the wear been taking place?  The statue might be 1000 years old (with a most probable sculptor active before the year 1300), but the  pilgrimage industry is much more vigorous with the advantages of modern travel.  Ten years is clearly too short.  Call it 100 years.
So with these ballpark estimates, we have a centimeter of the statue removed by $10^7$ touches, or each touch shortening the statue by a nanometer.  Pure copper has a lattice spacing of about 0.36 nm; our order-of-magnitude estimate is consistent with the "average touch" removing one-ish layers of copper atoms from the bronze of the statue.  That size of an effect seems much easier to imagine causes for.
