If an atom has an additional neutron compared to another, and is thus heavier, who's to say which should be recognised as the true element? So the atomic mass of an element in the periodic table is average mass with different isotopes present.
For example Iodine has about 37 different isotopes all with different atomic masses.
All have 53 protons but the neutron count varies from 55 to 91. Iodine-127 is stable but the rest are unstable especially Iodine-131 (much in the news lately as a radioactive pollutant of Japanese drinking water)