Q:

Why is cognitive maturity related to organism lifespan in larger animals and mammals?

I am not a student of biology, so I should provide some context to me asking this rudimentary question. While doing a graduate-level course on Reinforcement Learning, the instructors focused on how we as mammals have such amazing intellectual potential and how we tend to learn by examples of outcome based on our actions. This set me thinking about the high disparity between different species of multicellular organisms in how we mature.
I would state a couple of examples to back my point, I am unsure if this list is conclusive or not.
Elephants(Average Lifespan: 60-70 years): Elephant babies tend to stick to their families until they generally mature.
Humans(Average Lifespan: 70-80 years): Human babies are generally dependent on their parents for at least 8-12 years before they start demonstrating some intellectual maturity, which is a good 10-15 percent of their average lifespan)
Birds(Average lifespan is species-dependent, but assuming a 10-year span): Bird offsprings are extremely fast learners and tend to veer off independently within months of their birth.
Fishes (Medium to short lifespan): Not an extremely well-publicized parenting method for their offspring. Fishes learn to swim and hunt for food at extremely young ages, which is a sign of cognitive maturity.
Insects (Short Lifespan): Generally parenting is related to feeding offsprings for a short while before they become entirely independent.
As can be observed, the general span for the attainment of cognitive maturity in such organisms seems to be an inverse function of the average lifespan of the parent, and I wonder, what could be the reason for it? 
I absolutely apologize for any inaccuracies I might have cited because what I state is purely from a layman's observational perspective. I would be delighted to know what the bright folks here have to say on this matter.

A:

This answer might not completely answer your question, since this just explains the case in humans, but I think you can give this a read while waiting for a more accurate one. I would recommend you to read this amazing paper.
Generally, across animal species, the longer it takes an organism to reach maturity, the longer it lives. How the timing of onset of maturity relates to longevity in humans, is still a matter of debate. In this regard, it is of special interest whether the onset of intellectual maturity is associated with longevity, as the brain and associated parts of the central nervous system comprise an organ system that is widely thought to have played a vital role in humans’ evolutionary success.
First, they talk about defining cognitive maturity:

It would seem intuitive to define intellectual development as that part of the lifespan in which ability increases and intellectual maturity as that part in which ability plateaus or decreases. In such a model, an inflection point or peak in ability would mark the onset of intellectual maturity. It is unlikely, however, that the multidimensional abilities of composing and writing reach their peaks when a composer's or writer's work is made public for the first time. Rather, we regard maturity as a state that is attained when a certain relevant threshold is crossed, regardless of whether ability increases after that point.

Looking into the case of humans, it may be either a genetic mechanism or plasticity that couples rate of development and maintenance and repair. In the former scenario, genes that alter the rate of development such that maturity is reached earlier, would have as a concomitant effect the downregulation of maintenance and repair, leading to a shorter lifespan. (This is a shortened version- please go through the paper for more detail)
They conclude stating that the onset of intellectual maturity is associated with longevity. So, you are right about cognitive maturity of an organism being related to its age, and it points out to a really interesting result- blooming composers and writers live longer than child prodigies- as pointed out in a paper in ResearchGate.
What could be the reason for it? American psychologist Jerome Bruner proposed the purpose of the period of immaturity as being a time for experimental play without serious consequences, where a young animal can spend a great deal of time observing the actions of skilled others in coordination with oversight by and activity with its mother. So, there is the obvious need for a period of immaturity and this varies amongst different mammals. (source) 

