Because they can, or possibly because they have to.
Let me explain:
First of all, isotopes are simply atomic nuclei with the same number of protons and different numbers of neutrons. They may range anywhere from stable isotopes to those that last less than 10^-14 seconds. With today’s knowledge of nuclear science, it is not very difficult to add a neutron to a nucleus and produce an isotope, even if its lifetime is fleeting.
Perhaps you were referring more to isotopes in nature. In that case, the answer is more difficult but still centers around the concept of “because they can/have to”. ‘Heavy’ nuclei are formed within stars via two main processes, the r process and the s process. The difference between these processes is not important; however they both involve the absorption of neutrons by nuclei followed by beta decay (the process by which a neutron in the nucleus is converted into a proton or vice verse). In large stars, there are enough neutrons that a nucleus can absorb many neutrons before it has time to decay. Depending on the number of neutrons absorbed, the isotope of the final product can vary.
Unfortunately, if you are looking for a more in depth answer, then we must begin delve into nuclear physics (always a fun topic
). The stability of a nucleus is governed largely by the binding energy which incorporates the volume, surface, coulomb, symmetry and pairing energy of the nucleons. Each of these terms is dependent upon the mass and charge of the nucleus. Without going into the physics involved, since five different terms determine the stability of the nucleus, it is possible to come to several answers for each mass or charge that will result in ‘stable’ nuclei. Ergo, Isotopes.