The too-long-didn't-read (TLDR) of this letter is Seneca making the point that the study of wisdom and leading a wise life ought to be preeminent. While the vocational learning may lead us to leading a wise life, it is less important.
Towards the beginning of the letter he writes of liberal and vocational studies:
Such studies are profit-bringing occupations, useful only in so far as they give the mind a preparation and do not engage it permanently. ... they are our apprenticeship, not our real work.
Said differently, the studies which lead to a living (e.g. a career or job) are simply a means to an end. The end and primary focus ought to be the study of philosophy.
But there is only one really liberal study, – that which gives a man his liberty. It is the study of wisdom, and that is lofty, brave, and great-souled. All other studies are puny and puerile.
Certain persons have made up their minds that the point at issue with regard to the liberal studies is whether they make men good ... But which of these paves the way to virtue? ... what is there in all this that rids one of fear, roots out desire, or bridles the passions?
This is the sum-total of the letter. The rest of it delves into various examples and rifts of the same tune.
Whether you study Homer, Hesiod, Hecuba, Helen, Achilles, Patroclus, Ulysses (Odysseus), music, math, business, real estate, farming, astronomy, medicine, carpentry or physics, nothing is as important is the study of living and dying well - which is philosophy.
In each of the examples above, he contrasts the learning of subjects with the learning of philosophy. If, you learn something about one of the above subjects and can also apply that lesson to the study and learning of philosophy, perhaps there is use. But all learning ought to be focused on wise living.
Below are various examples or questions which put the focus of learning on philosophy.
What, in your opinion, I say, would be the point in trying to determine the respective ages of Achilles and Patroclus? Do you raise the question, "Through what regions did Ulysses stray?" instead of trying to prevent ourselves from going astray at all times?
Show me rather, by the example of Ulysses, how I am to love my country, my wife, my father, and how, even after suffering shipwreck, I am to sail toward these ends, honourable as they are. Why try to discover whether Penelope was a pattern of purity, or whether she had the laugh on her contemporaries? Or whether she suspected that the man in her presence was Ulysses, before she knew it was he? Teach me rather what purity is, and how great a good we have in it, and whether it is situated in the body or in the soul.
And instead of going one by one, contrasting vocational questions with philosophical questions, I'll simply note the questions which philosophy attempts to answer.
[how to] bring my soul into harmony with itself, and let not my purposes be out of tune ... how, in the midst of adversity, I may keep from uttering a doleful note ... how to lay out what is enough for a man to own. ... how useless property is to any man who would find it the greatest misfortune if he should be required to reckon out, by his own wits, the amount of his holdings ... how to share it with my brother? ... how to lose [my lands] with a light heart ... how great [the mind] is, or how puny! You know what a straight line is; but how does it benefit you if you do not know what is straight in this life of ours?
I await the future in its entirety; and if there is any abatement in its severity, I make the most of it. If the morrow treats me kindly, it is a sort of deception; but it does not deceive me even at that. For just as I know that all things can happen, so I know, too, that they will not happen in every case. I am ready for favourable events in every case, but I am prepared for evil.
Liberal or vocational studies do have value and Seneca notes them.
"do the liberal studies contribute nothing to our welfare?" Very much in other respects, but nothing at all as regards virtue. For even these arts of which I have spoken, though admittedly of a low grade – depending as they do upon handiwork – contribute greatly toward the equipment of life, but nevertheless have nothing to do with virtue. And if you inquire, "Why, then, do we educate our children in the liberal studies?" it is not because they can bestow virtue, but because they prepare the soul for the reception of virtue. Just as that "primary course," as the ancients called it, in grammar, which gave boys their elementary training, does not teach them the liberal arts, but prepares the ground for their early acquisition of these arts, so the liberal arts do not conduct the soul all the way to virtue, but merely set it going in that direction.
In sum, vocational studies and living prepare us to study the virtuous life - a philosophical life.
Philosophy alone delves into the question of the good.
There is but one thing that brings the soul to perfection – the unalterable knowledge of good and evil. But there is no other art which investigates good and evil.
And the good is found in excellence of soul and character. And what leads to this excellence? Moral virtues. He spends some words discussing some important virtues.
Bravery is a scorner of things which inspire fear; it looks down upon, challenges, and crushes the powers of terror and all that would drive our freedom under the yoke.
Loyalty is the holiest good in the human heart.
Temperance controls our desires; some it hates and routs, others it regulates and restores to a healthy measure, nor does it ever approach our desires for their own sake. Temperance knows that the best measure of the appetites is not what you want to take, but what you ought to take.
Kindliness forbids you to be over-bearing towards your associates, and it forbids you to be grasping.
[philosophy teaches] teach simplicity, moderation and self-restraint, thrift and economy, and that kindliness which spares a neighbour's life as if it were one's own and knows that it is not for man to make wasteful use of his fellow-man.
Wisdom is a large and spacious thing. It needs plenty of free room. One must learn about things divine and human, the past and the future, the ephemeral and the eternal; and one must learn about Time.
Because there is so much to learn and practice in the art of living well, we ought to minimize the superfluous to be able to focus on the most important and only allow the essential study of vocational arts into our life.
And in order that these manifold and mighty subjects may have free entertainment in your soul, you must remove therefrom all superfluous things. Virtue will not surrender herself to these narrow bounds of ours; a great subject needs wide space in which to move. Let all other things be driven out, and let the breast be emptied to receive virtue. "But it is a pleasure to be acquainted with many arts." Therefore let us keep only as much of them as is essential.
He opines on the people who desire to chase endless studies of vocational practices.
This desire to know more than is sufficient is a sort of intemperance. Why? Because this unseemly pursuit of the liberal arts makes men troublesome, wordy, tactless, self-satisfied bores, who fail to learn the essentials just because they have learned the non-essentials.
Our mortal time is limited and everything which we do or study ought to be considered through the lens of limited time. Therefore, prioritize the important over the unimportant.
Have I so far forgotten that useful saw "Save your time"? Must I know these things? And what may I choose not to know? ... Apply the measure to the years of your life; they have no room for all these things.
He next takes aim at useless studies under the domain of philosophy.
I have been speaking so far of liberal studies; but think how much superfluous and unpractical matter the philosophers contain! Of their own accord they also have descended to establishing nice divisions of syllables, to determining the true meaning of conjunctions and prepositions; they have been envious of the scholars, envious of the mathematicians. They have taken over into their own art all the superfluities of these other arts; the result is that they know more about careful speaking than about careful living.
He takes so much umbrage with the study of these fluffy topics, he places them in a new category: non-knowledge.
The Pyrrhonean, Megarian, Eretrian, and Academic schools are all engaged in practically the same task; they have introduced a new knowledge, non-knowledge.
Speaking of these various philosophy schools, he wonders if it's better to sit in the dark or to have our eyes gouged out.
It is better, of course, to know useless things than to know nothing. One set of philosophers offers no light by which I may direct my gaze toward the truth; the other digs out my very eyes and leaves me blind. ... The whole universe is then a vain or deceptive shadow. I cannot readily say whether I am more vexed at those who would have it that we know nothing, or with those who would not leave us even this privilege.