Why does radioactive decay happen?

The second law of thermodynamics says that entropy (disorder) always increases (universally). A "radioactive" isotope of an element is one in which the balance of attractive forces holding the nucleus together with the repelling forces of the constituent particles is just stable enough to prevent an immediate breakdown of the element, but not stable enough to stop the gradual release of energy to reach a more stable final elemental state.

It's something like a herd of cows packed tightly into a yard, which has one broken section of fence. The cows are "stable" in the enclosure, but the pressure of them (order) will constantly try to decrease (disorder). They can't all just fall through the broken part of the fence, and they can't go through in sequence, because they need to be lined up just right for one to get out.

So, periodically and statistically regular, one cow gets out, changing the structure of the herd slightly. At a later time another one will get out. This will continue until the herd reaches a size "stable" with the fence, and no more will be forced out.