A method for preparing a superoxide-generating composition, the method comprising the steps of: attaching a superoxide-generating compound to the surface of a first silica precursor to form a core; and coating the outer surface of the core with a shell having a calcium compound attached to the surface of a second silica precursor to form a shell; wherein step S100 comprises the steps of: mixing and dispersing 30-40 parts by weight of the first silica precursor in 100 parts by weight of distilled water to obtain a dispersion; wherein the first silica precursor is a silica sol obtained by mixing 20-40 wt% of silicon oxide powder having a particle size of 0.2-1.0 μm with 60-80 wt% of water; dissolving 5-10 parts by weight of the superoxide-generating compound in 100 parts by weight of distilled water to obtain an aqueous solution; wherein the superoxide-generating compound is one or a combination of two or more selected from among silver nitrate (AgNO3), gold chloride (AuCl3, HAuCl4), and platinum chloride (PtCl4); and adding and dispersing 10-30 parts by weight of the aqueous solution of step S120 to 100 parts by weight of the dispersion of step S110; wherein step S200 comprises the steps of: dissolving 5-10 parts by weight of the calcium compound in 100 parts by weight of distilled water to obtain an aqueous solution; adding and dispersing 1-5 parts of the aqueous solution of step S210 in 100 parts by weight of the core of step S100 to obtain a dispersion; and adding and reacting 120-150 parts by weight of the second silica precursor to and with 100 parts by weight of the dispersion of step S220 to gel the dispersion. attaching a superoxide-generating compound to the surface of a first silica precursor to form a core; and coating the outer surface of the core with a shell having a calcium compound attached to the surface of a second silica precursor to form a shell; wherein step S100 comprises the steps of: mixing and dispersing 30-40 parts by weight of the first silica precursor in 100 parts by weight of distilled water to obtain a dispersion; wherein the first silica precursor is a silica sol obtained by mixing 20-40 wt% of silicon oxide powder having a particle size of 0.2-1.0 μm with 60-80 wt% of water; dissolving 5-10 parts by weight of the superoxide-generating compound in 100 parts by weight of distilled water to obtain an aqueous solution; wherein the superoxide-generating compound is one or a combination of two or more selected from among silver nitrate (AgNO3), gold chloride (AuCl3, HAuCl4), and platinum chloride (PtCl4); and adding and dispersing 10-30 parts by weight of the aqueous solution of step S120 to 100 parts by weight of the dispersion of step S110; mixing and dispersing 30-40 parts by weight of the first silica precursor in 100 parts by weight of distilled water to obtain a dispersion; wherein the first silica precursor is a silica sol obtained by mixing 20-40 wt% of silicon oxide powder having a particle size of 0.2-1.0 μm with 60-80 wt% of water; dissolving 5-10 parts by weight of the superoxide-generating compound in 100 parts by weight of distilled water to obtain an aqueous solution; wherein the superoxide-generating compound is one or a combination of two or more selected from among silver nitrate (AgNO3), gold chloride (AuCl3, HAuCl4), and platinum chloride (PtCl4); and adding and dispersing 10-30 parts by weight of the aqueous solution of step S120 to 100 parts by weight of the dispersion of step S110; wherein step S200 comprises the steps of: dissolving 5-10 parts by weight of the calcium compound in 100 parts by weight of distilled water to obtain an aqueous solution; adding and dispersing 1-5 parts of the aqueous solution of step S210 in 100 parts by weight of the core of step S100 to obtain a dispersion; and adding and reacting 120-150 parts by weight of the second silica precursor to and with 100 parts by weight of the dispersion of step S220 to gel the dispersion. dissolving 5-10 parts by weight of the calcium compound in 100 parts by weight of distilled water to obtain an aqueous solution; adding and dispersing 1-5 parts of the aqueous solution of step S210 in 100 parts by weight of the core of step S100 to obtain a dispersion; and adding and reacting 120-150 parts by weight of the second silica precursor to and with 100 parts by weight of the dispersion of step S220 to gel the dispersion.