It says equal volumes of all gasses under same conditions of temp. and pressure contains the same number of atoms/molecules.
Now suppose you have 1L of Chlorine in a box and 1L Hydrogen in another box , now the comparitively huge size of the Cl atom means less of it will fit in the box , whereas lots of hygrogen will. ( breaking the law)
But, well this should have an effect in pressure , how does all that boil down to avogadro being right ?