Isn't that true of anything in science? Or life, for that matter...That is why I always note the only thing written in stone is aquatics is "Nothing is written in stone."
Actually the same is true of most if not all mammals, amphibians, eh, anything that grows really. Cell division rates are influenced temperature in most organisms, with rates increasing as temperatures go up. This happens for the same reason activity in pretty much all fauna increases with temperature - warmth is a form of energy, any activity taking place under colder condition will either cost more energy to get started because warmth is required to get it going (endothermic reactions) or will be less efficient because a larger portion of the energy input converts into heat rather than other types (e.g. kinetic) making the activity more costly (exothermic reactions). This is up to a certain tipping point that differs per organism depending on among other things how they regulate temperature, after which further temperature increases very rapidly lead to destruction of the organism (for people, think of running a fever - there is only so many degrees you can go over your natural body heat before things turn critical).This is true - higher temps = higher metabolism = shorter lives. Fast growers tend to have shorter lives compared to runts or those that grew at a normal rate. Breeders have shorter lives, especially if excessively bred. . . . . But I don't know why - don't know the science behind it.
Increased cell division rates cause more rapid growth, faster bodily processes, higher energy levels, etc. However, unfortunately cells have a set, limited number of times they can divide before that strain of cells runs out of divisions and that is the end for that strain. So if your liver cells run near the end of their set number of divisions, your liver starts to give out. The slower cells divide, the longer it takes to reach that point in time and vice versa.
This has actually been equally proven for people. Being too active (e.g. fanatic sports person) tends to shorten your lifespan. For other, more obvious reasons though, going to the opposite extreme is also bad for your health. In other words, the golden middle is what you're looking for.
As for the breeding - the shortened life span in this case is more likely due to constant stress and over exhaustion. Breeding is the life goal and so disproportionate amounts of energy tend to go into making it a resounding success, whether at the cost of the parent or not. Bettas being kept by serious breeders are probably bred more more often than natural, full recuperation would allow (not to say that in nature things would be better, there equally the survival of the largest amount of fry is likely more important to the betta than potential costs to its own life span).