What makes protons give the property of acidity?
While it is true that oxidizing strong acids like nitric and sulfuric are more corrosive than a non-oxidizing strong acid like hydrochloric, the latter still is able to dissolve materials (e.g, metals, minerals, proteins) and cause burns to the skin. A strong acid like HCl can (in the case of human skin or other biological materials) catalyze the hydrolysis of proteins, fats, and carbohydrates down to their water-soluble components. This is what happens in your stomach, where there is an abundance of hydrochloric acid, as well as enzymes to speed up the process.

The most widely accepted measure of how strong an acid is, its its acid dissociation constant, not the pH of a solution of it.