The theme of this letter is oikeiôsis. William O. Stephens has a fine explanation of this concept in this Stoic Ethics entry, under the section Theory of Appropriation.
Seneca, in this letter, is exploring the question "what is best suited for man" or in other words, what is appropriate for man?
He delves into the concept of oikeiôsis by observing the nature of self-preservation in animals. Understanding this, will help the Stoic student understand what is the unique nature of a fully grown, human adult.
The big point of this letter is to prove that there is something inborn and inherent to all animals, which helps them to want to survive and exist. And this is not learned, but is something entwined with existence from the day the animal is born. And that thing is the instinct to exist; to live; to survive.
The instinct pushes beyond the experience of pain.
The proof that it is not fear of pain which prompts them thus, is, that even when pain checks them they struggle to carry out their natural motions. Thus the child who is trying to stand and is becoming used to carry his own weight, on beginning to test his strength, falls and rises again and again with tears until through painful effort he has trained himself to the demands of nature.
And, there are some things about our nature that we simply know or feel, yet cannot fully explain.
Nature is easier to understand than to explain; hence, the child of whom we were speaking does not understand what "constitution" is, but understands its own constitution.
We also know that we possess souls, but we do not know the essence, the place, the quality, or the source, of the soul.
Everyone of us understands that there is something which stirs his impulses, but he does not know what it is. He knows that he has a sense of striving, although he does not know what it is or its source.
The human has his or her own instincts and appropriations based on the stages of growth. It takes a lot of work to develop into a full human being and it's probable that some humans, despite their age, never fully blossom. But, the human does go through stages and has the tools suited to him or her in order to grow into their next stage. Seneca uses teeth as an example.
But each age has its own constitution, different in the case of the child, the boy, and the old man; they are all adapted to the constitution wherein they find themselves. The child is toothless, and he is fitted to this condition. Then his teeth grow, and he is fitted to that condition also.
The periods of infancy, boyhood, youth, and old age, are different; but I, who have been infant, boy, and youth, am still the same
He then summarizes the point.
For even if there is in store for him any higher phase into which he must be changed, the state in which he is born is also according to nature. First of all, the living being is adapted to itself, for there must be a pattern to which all other things may be referred. I seek pleasure; for whom? For myself. I am therefore looking out for myself. I shrink from pain; on behalf of whom? Myself. Therefore, I am looking out for myself. Since I gauge all my actions with reference to my own welfare, I am looking out for myself before all else. This quality exists in all living beings – not engrafted but inborn.
He further explores other animals who have inborn instincts for survival.
Why should the hen show no fear of the peacock or the goose, and yet run from the hawk, which is a so much smaller animal not even familiar to the hen? Why should young chickens fear a cat and not a dog? These fowls clearly have a presentiment of harm – one not based on actual experiments; for they avoid a thing before they can possibly have experience of it.
Hence indeed it is evident that these animals have not reached such a condition through experience; it is because of an inborn desire for self-preservation.
each animal at the same time consults its own safety, seeking that which helps it, and shrinks from that which will harm it. Impulses towards useful objects, and revulsion from the opposite, are according to nature; without any reflection to prompt the idea, and without any advice, whatever Nature has prescribed, is done.
He concludes with a bit more evidence about how some insects perform their seemingly incredible arts, which they are born with. The bees can make honeycomb cells and the spiders can make immaculate webs - "This art is born, not taught."
We are born with an inherent instruction book to prompt us to take care of ourselves.
Nature has communicated nothing except the duty of taking care of themselves and the skill to do so; that is why living and learning begin at the same time.
This is the first equipment that Nature granted them for the maintenance of their existence – the quality of adaptability and self-love. They could not survive except by desiring to do so.