Have a look at the binding energy per nucleon curve:
There are many stable configurations below iron, so the binding energy is not the only criterion for stability.
Graph of nuclides (isotopes) by type of decay. Orange and blue nuclides are unstable, with the black squares between these regions representing stable nuclides. The unbroken line passing below many of the nuclides represents the theoretical position on the graph of nuclides for which proton number is the same as neutron number. The graph shows that elements with more than 20 protons must have more neutrons than protons, in order to be stable.
The stability is a balance between the repulsive forces from positive charges and the attraction of the nuclear force. It is a many body problem that has stable solutions for certain configurations of protons and neutrons and unstable ones where either the repulsion of too many protons is strong, or the number of neutrons gets too large and neutron decay channels open up.
In general a decay will occur if the nucleus is not in the lowest minimum of energy, but there exists a configuration of subsets of its nuclei that will give an overall lower energy state.
Classically it is called a metastable state and is illustrated by:
Quantum mechanically there exists a probability that the decay will occur to the lower energy configuration, and this probability is connected with the lifetime of the decay.
There exists an extensive article in wikipedia on radioactive decays and the various possibilities.