I've seen the graphs of the stability line but I can't find any reason as to why this happens, I understand radiation, just not why radiation needs to occur in the first place if that makes sense.
The nuclear force only acts between nearest neighbors to hold them together- but the electrostatic force driving them apart has infinite range, so any one proton in the nucleus feels the repulsion of all the other protons. This is why you need extra neutrons (which bind via the nuclear force but do not experience the electrostatic force) as "glue" to keep all the protons stuck together.
Having a stable nucleus is a complex balance between the
- residual nuclear interaction attracting protons and neutrons together, but has quite short range even for the nuclear scale
- electrostatic interaction (trying to fly the protons apart, but not acting on neutrons),
- weak interaction, able to convert protons into neutrons and neutrons in protons if it happens to be energetically favorable
- Pauli principle that prevents neutrons and protons (it acts separately for protons and neutrons) clumping too close together
...as well as some other factors that have less of influence.
The first two factors together act as if you need to "dilute" protons with neutrons in order to keep them from flying away, but not too much.
These two factors have different behavior at a distance.
The important part is, the electrostatic interaction has relatively longer range. (In fact, both interactions are good to infinity, but the electrostatic weakens with distance much slower)
As you grow the nucleus bigger and bigger, the electrostatic interaction gets more and more influence in the overall balance, because it acts better at a distance.
This is why bigger nuclei favor more neutrons.