Protons don't like each other. Naturally, 'positive charges repel', so it wouldn't be possible to have more than one proton in the nucleus. Here's where the neutron comes in. When atoms are created by fusion, neutrons are included in this process. In this process of fusion, the building blocks of the nucleus are squished together, and all the particles undergo a mass change. Each nucleon loses a small amount of mass, mass which is converted into nuclear binding energy or nuclear glue. It's this material that keeps the protons and neutrons together, making the nucleus relatively stable. Protons alone couldn't engage in this process, because it takes both nucleons to contribute to the creation of this 'binding energy' that allows the nucleus to fuse together.