why do elements have isotopes?

Isotopes are defined as different atoms of same element which have same number of electrons and protons,but different numbers of neutrons or we can also defined isotopes have same atomic number but different atomic mass.For ex- ₆C¹²,₆C¹³,6C¹⁴ and ₁₇Cl³⁵ and₁₇Cl³⁷ etc.Since isotopes have the same number of electrons,which shows that they all behave almost the same in chemical reactions.
The number of protons in an atom of an element is constant like carbon always has 6 protons.Therefore,they also have 6 electrons to balance out the charge of the atom.But number of neutrons may vary between atoms,which affects the mass number of the atom.Since the mass number is equal to the number of protons and neutrons (since electrons have very little mass).So carbon always has 6 protons, but it can have 6 or 7 or 8 neutrons,giving the atoms mass numbers of 12,13 or 14 (respectively).Since they are all carbon (because of the 6 protons), then they are considered isotopes of each other.Also the chemical properties of an element solely determined by the no. of protons and electrons,different no. of neutrons neither change the element nor its chemical properties.