Through those near to Me I show Myself holy,
And gain glory before all the people.”And Aaron was silent.
WHY WAS AARON SILENT?
Ramban on Leviticus 10:3:2
VAYIDOM AHARON’ (AND AARON WAS SILENT). This means that he had cried aloud, but then he became silent.
Rabbeinu Bachya on Leviticus 10:3
“Aaron remained silent.” Silence is one of the ways in which mourning is expressed
וידם אהרן AND AARON WAS SILENT — He received a reward for his silence. And what was the reward he received? That the subsequent Divine address was made to him alone and not to Moses also.
(13) Rabbi Akiva says: A safeguarding fence around wisdom is silence.
Rabbi Jonathan Kraus, "Sh’tikah—What Kind of Silence?" in Block, Rabbi Barry H.. The Mussar Torah Commentary: A Spiritual Path to Living a Meaningful and Ethical Life (p. 162). CCAR Press.
Aaron’s response exemplifies the ideal response to any experience of God’s strict justice (tziduk hadin) and adds that we should respond with silence when we hear others insulting us, rather than acting on our understandable impulse to respond in kind. The Rabbis lift up the practice of restraint—the capacity for self-awareness and control over one’s verbal impulses—as a sign of strong character and the capacity for wisdom. They interpret Aaron’s silence as an impressive sign of self-restraint.
When silence is not a virtue
Rabbi Jonathan Kraus, "Sh’tikah—What Kind of Silence?"
Shortly after this incident, when Moses chastises Aaron’s remaining sons, Eleazar and Ithamar, for not eating their portion of the community’s sin offering, Aaron finds his voice again. It is Aaron who responds calmly and rationally, reminding Moses that it could hardly have been appropriate for him and his remaining sons to partake of the sin offering at that moment when God was so obviously displeased with their service. And Moses concurs (Leviticus 10:19–20). If Aaron’s previous silence really was a reflection of a broken heart, how does he so quickly find the capacity both to make a dispassionate analysis of what’s ritually appropriate and to respond so calmly to his angry younger brother? And speaking of Eleazar and Ithamar: Might Aaron’s remaining sons not need their father to voice some feeling, some sense of loss, some acknowledgment of the terrifying, shattering, possibly unjust loss of their two older brothers? Is Aaron’s silence a sign of his pious virtue or a reflection of his limitations as a father?
A time for silence and a time for speaking;
Alan Morinis. Everyday Holiness, p.140
In the book of Job, after listening to his so-called friends trying to comfort him, Job finally erupts with: “Be silent and I will teach you wisdom.” In silence is wisdom, too. A wise person, therefore, is one who knows what to say and when to say it but also knows when to keep silent. And even a fool is judged wise just because he keeps silent.
Megilla 18a: 11
What is the meaning of that which is written: “For You silence is praise” (Psalms 65:2)? The best remedy of all is silence, i.e., the optimum form of praising God is silence. The Gemara relates: When Rav Dimi came from Eretz Israel to Babylonia, he said: In the West, Eretz Yisrael, they say an adage: If a word is worth one sela, silence is worth two.
Alan Morinis. Everyday Holiness (pp. 144-145).
The Mussar masters are referring to a silence that is life giving, not death dealing, entered voluntarily in pursuit of spiritual insight and wisdom. This is contemplative silence, taken on voluntarily as spiritual practice. A soul deprived of silence loses track of itself. It is afflicted. Sooner or later, it will in desperation seek its need, or capitulate to negative forces.