Our Gemara on Amud Aleph employs a proof text from Psalms (38:14) to define the Hebrew words "Cheresh" as someone who is deaf and "Ilem" as a mute who does not speak:

וַאֲנִ֣י כְ֭חֵרֵשׁ לֹ֣א אֶשְׁמָ֑ע וּ֝כְאִלֵּ֗ם לֹ֣א יִפְתַּח־פִּֽיו׃

"But I am like a deaf man, unhearing, like a dumb man who cannot speak up."

In the face of mistreatment, the question arises: When is it proper to speak up, and when is it proper to either ignore or forgive?

Rambam (Laws of Deos 6:6) states:

"When one person wrongs another, the latter should not remain silent and despise him, as [II Samuel 13:22] states concerning the wicked: 'And Avshalom did not speak to Amnon, neither good, nor bad, for Avshalom hated Amnon.' Rather, he is commanded to make the matter known and ask him: 'Why did you do this to me?' 'Why did you wrong me regarding that matter?' as [Leviticus 19:17] states: 'You shall surely admonish your colleague.'”

Is it an extra act of piety to choose to forgive and not speak up? At first glance, it would seem that this is what the Gemara (Rosh Hashanah 17a) means when it says:

"רָבָא אָמַר: כׇּל הַמַּעֲבִיר עַל מִדּוֹתָיו — מַעֲבִירִין לוֹ עַל כׇּל פְּשָׁעָיו"

Rava understood this verse differently and said: With regard to whoever forgoes his reckonings with others for injustices done to him, the heavenly court, in turn, forgoes punishment for all his sins.

Even if this is true, one must be careful about deluding oneself into thinking they are pious and forgiving until they suddenly blow up with repressed rage over a series of past misdeeds. The other person was unaware of all these transgressions as you were avoidant of discussing it, possibly for less than pious reasons (see Arakhin 16b, which might be referring to this when it uses the term, "Anava Shelo Lishmah").

However, I do not believe this to be true. Here is how the Rambam formulates this (ibid 6:9):

"If a person who was wronged by a colleague would rather not admonish him or mention the matter at all because the person who wronged him was very boorish or because he was mentally disturbed, [provided] he forgives him totally without bearing any feelings of hate or admonishing him, it is an act of piety. The Torah is concerned only with those who carry feelings of hate."

The implication is that the preferred path is to confront the other person as long as it is done with respect. It is considered an extra pious act to let go and forgive if the person was not likely to be receptive. (Avodas Hamelech on the Rambam agrees with this interpretation.) Rashi’s choice of words in Rosh Hashanah (17a) seems to also indicate that the pious standard is not absolute silence in the face of humiliation, though his formulation is not like the Rambam, :

"המעביר על מדותיו - שאינו מדקדק למדוד מדה למצערים אותו ומניח מדותיו והולך לו"

One who overcomes his personal temperament: someone who is not exacting to make sure to give back in-kind to those who distress him. Instead, he stays calm and carries on without confrontation.

Rashi implies that it is a relative matter: "He does not give back in kind." This extra phrase suggests that his response should be measured but perhaps not without any attempt at clarifying or assertiveness.

You might wonder, let us say you are not such a pious individual, and you do not want to overlook this insult, and you still don't believe the person will take the confrontation well. Is it permitted by the Torah to confront the person anyway? Quite possibly. After all, that is why it is considered an extra pious act to abstain from saying anything. Or, maybe one must keep quiet if there is a strong likelihood of ugly conflict, and the extra piety involves not resenting the person and forgiving them as opposed to hating them. Sefer Yereim (195) does seem to say that if you make reasonable effort to inform somebody that they hurt you, and they remain hostile and not contrite, at that point there is no prohibition against hating them because they are a sinner and a violator.

One important point to consider is that even if the person is now labeled a sinner and is permitted to be hated in a sense of loathing and disgust, we are still obligated to show kindness towards a person in terms of our behavior. Rambam (Laws of Murder 13:14) states:

"The enemy mentioned in the Torah is not a gentile but rather a Jew. One might ask: How is it possible for one Jew to hate another? Is it not written Leviticus 19:17: 'Do not hate your brother in your heart'? Our Sages explained that this is referring to a person who, while alone, sees a colleague violate a transgression and rebukes him, but the colleague did not cease transgressing. In such an instance, it is a mitzvah to hate the person until he repents and abandons his wickedness. Even if he did not repent yet, if one sees him in panic because of his cargo, it is a mitzvah to unload and reload with him, instead of leaving him inclined toward death, lest he tarry because of his money and be brought to danger. For the Torah showed concern for the lives of the Jewish people, both the wicked and the righteous, for they are attached to God and believe in the fundamentals of our faith. 

Also, at the moment that a person is being attacked, it may be permitted to fire back in kind, because it is considered self defense, (See Shemiras Halashon, Be’er Mayim Chayyim, Lavin 8:4). Of course, judgment and discretion should be used. Not everything that is permitted is smart to do relationship wise.

One final point regarding the verse quoted in our Gemara. This verse indicates two processes: (1) to practice holding back from speaking when insulted or shamed but also (2) to not even hear the insult in the first place.

Tzror Hamor (Bereishis 3:7) speaks of this idea, that the pious person doesn’t even see or notice mundane matters so he is insulated from certain griefs. This is why Adam and Chavah are described as having “their eyes opened “ after they ate from the Tree of Knowledge. They started to notice the various distractions of the world. 

As Sefer Hachinuch (241) counsels, how you perceive what is happening can help manage the hurt and anger:

מִשָּׁרְשֵׁי הַמִּצְוָה. שֶׁיֵּדַע הָאָדָם וְיִתֵּן אֶל לִבּוֹ כִּי כָּל אֲשֶׁר יִקְרֵהוּ מִטּוֹב עַד רַע, הוּא סִבָּה שֶׁתָּבוֹא עָלָיו מֵאֵת הַשֵּׁם בָּרוּךְ הוּא. וּמִיַּד הָאָדָם מִיַּד אִישׁ אָחִיו לֹא יִהְיֶה דָּבָר בִּלְתִּי רְצוֹן הַשֵּׁם בָּרוּךְ הוּא, עַל כֵּן כְּשֶׁיְּצַעֲרֵהוּ אוֹ יַכְאִיבֵהוּ אָדָם יֵדַע בְּנַפְשׁוֹ כִּי עֲוֹנֹתָיו גָּרְמוּ, וְהַשֵּׁם יִתְבָּרַךְ גָּזַר עָלָיו בְּכָךְ, וְלֹא יָשִׁית מַחְשְׁבוֹתָיו לִנְקֹם מִמֶּנּוּ, כִּי הוּא אֵינוֹ סִבַּת רָעָתוֹ, כִּי הֶעָוֹן הוּא הַמְּסַבֵּב, וּכְמוֹ שֶׁאָמַר דָּוִד עָלָיו הַשָּׁלוֹם (שמואל ב טז יא) הַנִּחוּ לוֹ וִיקַלֵּל כִּי אָמַר לוֹ יְיָ. תָּלָה הָעִנְיָן בְּחֶטְאוֹ וְלֹא בְּשִׁמְעִי בֶּן גֵּרָא. וְעוֹד נִמְצָא בְּמִצְוָה זוֹ תּוֹעֶלֶת רַבָּה לְהַשְׁבִּית רִיב וּלְהַעֲבִיר הַמַּשְׂטֵמוֹת מִלֵּב בְּנֵי אָדָם, וּבִהְיוֹת שָׁלוֹם בֵּין אֲנָשִׁים יַעֲשֶׂה הַשֵּׁם יִתְבָּרַךְ שָׁלוֹם לָהֶם.

It is from the roots of the commandment that a person know and put into his heart that everything that happens to him — good and bad — the cause of it coming to him is from God, blessed be He. And from the hand of man — from the hand of a man to his brother — there would not be anything without the will of God, blessed be He. Hence, when a person caused him pain or hurt him, he should know for himself that his [own] sins caused [it], and that God, may He be blessed, ordained this for him. And he should not place his thoughts to taking vengeance from [the one who pained him], since he is not the cause of his evil, but rather the sin is the cause; like David, peace be upon him, stated (II Samuel 16:11), “leave him to curse, since the Lord told him [so]” — he made the matter depend upon his [own] sin, and not upon Shimei ben Gera. And there is also a great benefit found in this commandment, in quieting a dispute and removing enmity from the heart of people. And when there is peace among people, God, may He be blessed, will make peace for them.