A play on one verb. Everything turns on the pair ἄρξεις — ἀρχθῇς: the active and the passive of one and the same ἄρχω. Neither Russian nor English has anything to render the figure with, and both translators break it into two different words: Rogovin "to teach / to have learned," Long "lay down rules / obey rules." The Greek says one word twice, and there the point lies: do not lead until you have been led.
The double sense of ἄρχω. The verb means both "to begin" and "to rule." Both senses work here: in letters you will not begin (to write and read on your own) until you have been taken in hand; and you will not become a teacher until you have been a pupil. Marcus picks a word that needs no qualifying: one and the same relation describes both instruction and authority.
Why an example from school. γράφειν καὶ ἀναγινώσκειν — "writing and reading," the most elementary schooling, what everyone has gone through. The argument is built not on the rare but on the notorious: no one disputes that letters are learned under another's hand. Hence the transition — τοῦτο πολλῷ μᾶλλον ἐν τῷ βίῳ, "much more so in life" — and the conclusion comes out not as an exhortation but as an inference.
To whom it is addressed. The passage is written by an emperor, that is, by a man who has no one to take an order from. So much the sharper: in his case ἄρχω means precisely "to rule," and the reminder to himself is that the right to lead is derivative of the experience of being led. Cf. 11.5 ("what is your craft? to be good" — and it comes about only out of θεωρήματα) and 10.16 (enough of discussing what a good man is like — be one). The governing discipline is action, the sustaining one assent.