Under Avogadro's law, equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

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Avogadro's law shows that at the same temperature and pressure, equal volumes contain the same number of molecules. This comes from the idea that pressure in a gas arises from collisions of many particles with container walls; if you fix temperature and pressure and compare different gases, the amount of stuff (the number of molecules) must be the same to maintain the same pressure in that volume. So, volume directly reflects the number of particles when T and P are held constant, regardless of the gas’s identity. This is the reason the statement is true.

Of course, this relies on ideal gas behavior. Real gases deviate from this picture at very high pressures or low temperatures because intermolecular forces and the finite size of molecules matter, but under typical conditions the relationship holds well. This concept underpins the idea that equal volumes at fixed T and P contain the same number of molecules, and it leads to the idea that one mole of any gas occupies the same molar volume at a given T and P.