if it is possible for a man's heart to contain submission and arrogance simultaneously Can submission and pride co-exist in the heart of the believer? I answer this as follows:
Any pride which stems from bodily things distances submission from the heart. It is impossible for both to co-exist simultaneously since they mutually repel each other. For if a man takes pride in any secular thing, what brings him to this pride is:
Rather, he will consider it that he himself is the creator of his good fortune, that he has acquired it with his own strength and ingenuity, as written about Sancheriv "by the strength of my hand I have accomplished" (Yeshaya 10:13), and about Nebuchadnezar "Is this not the great Babylon, which I built for a royal palace with the strength of my power and for the honor of my glory?" (Daniel 4:27), and Pharaoh "My river is my own..." (Yechezkel 29:3), and you already know what swiftly followed their boastful proclamations - the destruction of their kingdom and their land.
The reprehensible one - that a person prides himself on his wisdom or a righteous man on his good deeds. This causes the wisdom and righteousness to become magnified in his eyes, so that he is satisfied with what he has already accomplished, and thinks that it is enough for him the good reputation and praise he has achieved from his fellow men. This will cause him to look down on others, despise them, and speak badly of them, to belittle the wise men of his generation in his eyes, and glorify himself in the shortcomings and ignorance of other people. Our Rabbis of blessed memory call this: "one who seeks honor by putting down others (has no share in the world to come)". One like this will never be submitted nor humble.
The praiseworthy one - the pride of the wise man in his wisdom or of the righteous man in his good deeds when it is an expression of his gratitude to the Creator for helping him greatly on them, and of his joy in them. When it causes him to improve and continue exerting himself in them, and to be humble to his colleagues, happy with their success, and concerned for their honor. To not reveal their failings and to speak good of them. To love them and judge them favorably, and to be careful of their honor. All of his own good deeds will seem few in his eyes, and he will always exert himself to increase them. He will be humbled by his inability to reach his longing in them. He will lower himself before someone who he hopes will help him to increase in them. He will be grateful to G-d for having graced him with qualities and thanks Him for helping him to reach exalted levels.
This kind of arrogance (aggrandizing) is not detrimental to submission and does not repel it. The verse says of Yehoshafat "And his heart was uplifted in the ways of the L-ord" (Divrei Hayamim II 17:6), just the opposite - such pride helps humility and increases his submission as written "In the wake of humility comes fear of the L-ord, riches, honor, and life" (Mishlei 22:4).
אֲבָל אִם יִתָּכֵן לְהִתְקַבֵּץ בְּלֵב הַמַּאֲמִין הַכְּנִיעָה וְהַגַּאֲוָה אִם לֹא. אוֹמַר בִּתְשׁוּבַת זֶה:
if it is possible for a man's heart to contain submission and arrogance simultaneously
Can submission and pride co-exist in the heart of the believer? I answer this as follows:
כִּי הַגַּאֲוָה מִתְחַלֶּקֶת לִשְׁנֵי חֲלָקִים.
There are two categories of pride:
אֶחָד מֵהֶם גַּאֲוַת הָאָדָם בְּגוּפוֹ וּבְעִנְיְנֵי גּוּפוֹ וְתִקּוּנָיו הַגּוּפִיִּים.
(1) A man's pride in his body, and its conditions, or in all things that further his body's well being.
וְהַחֵלֶק הַשֵּׁנִי גַּאֲוָתוֹ בְּמַעֲלוֹתָיו הָרוּחָנִיּוּת בַּחָכְמָה וְהַמַּעֲשֶׂה הַטּוֹב בַּעֲבוּר עֲבוֹדַת הַבּוֹרֵא,
(2) A man's pride in his spiritual qualities - the wisdom used and good deeds he performed in the service of G-d.
וְכָל גַּאֲוָה שֶׁתִּהְיֶה מֵחֲמַת הַגּוּפִיִּים הִיא מַרְחֶקֶת הַכְּנִיעָה מִן הַלֵּב וּמִן הַנִּמְנָע הִתְקַבְּצָם בְּלֵב אֶחָד בַּעֲבוּר הַרְחָקַת כָּל אֶחָד מֵהֶם אֶת חֲבֵרוֹ, כִּי כַּאֲשֶׁר יִתְגָּאֶה הָאָדָם בְּדָבָר מִדִּבְרֵי הָעוֹלָם אֵין מְבִיאוֹ לָזֶה, אֶלָּא:
Any pride which stems from bodily things distances submission from the heart. It is impossible for both to co-exist simultaneously since they mutually repel each other. For if a man takes pride in any secular thing, what brings him to this pride is:
בְּזוֹת אֶת בַּעַל הַטּוֹבָה,
* belittling the Source of this good (G-d)
וּמִעוּטָהּ אֶצְלוֹ,
* downplaying the value of this good
וּמִעוּט יְדִיעָתוֹ בִּמְהִירוּת הֲסָרָתָהּ מִמֶּנּוּ וּנְסִיעָתָהּ מֵאֶצְלוֹ.
* little consciousness of how swiftly it can be taken from him or leave him.
וְיַחְשֹׁב כִּי הוּא הַמֵּטִיב בָּהּ לְעַצְמוֹ וְהַקּוֹנֶה אוֹתָהּ בְּכֹחוֹ וּבְחָכְמָתוֹ כמ״ש סַנְחֵרִיב (ישעיהו י׳:י״ג) בְּכֹחַ יָדִי עָשִׂיתִי וְאָמַר נְבוּכַדְנֶצַּר (דניאל ז) הֲלָא דָא הִיא בָּבֶל רַבְּתָא וְאָמַר פַּרְעֹה (יחזקאל כט) לִי יְאוֹרִי וְגוֹ׳. וּכְבָר יָדַעְתָּ מָה שֶׁהָיָה תֵּכֶף לְמַאֲמָרָם מֵהֲרִיסַת מַלְכוּתָם וְהַשְׁחָתַת מֶמְשַׁלְתָּם.
Rather, he will consider it that he himself is the creator of his good fortune, that he has acquired it with his own strength and ingenuity, as written about Sancheriv "by the strength of my hand I have accomplished" (Yeshaya 10:13), and about Nebuchadnezar "Is this not the great Babylon, which I built for a royal palace with the strength of my power and for the honor of my glory?" (Daniel 4:27), and Pharaoh "My river is my own..." (Yechezkel 29:3), and you already know what swiftly followed their boastful proclamations - the destruction of their kingdom and their land.
אַךְ הַגַּאֲוָה שֶׁבַּמַּעֲלוֹת הָרוּחָנִיּוֹת מִתְחַלֶּקֶת לִשְׁנֵי חֲלָקִים. אֶחָד מֵהֶם מְגֻנֶּה וְהַשֵּׁנִי מְשֻׁבָּח.
Pride in spiritual qualities divides into two categories, one reprehensible and one praiseworthy.
הַמְגֻנֶּה שֶׁיִּתְגָּאֶה הָאָדָם בְּחָכְמָתוֹ וְהַצַּדִּיק בְּמַעֲשֵׂהוּ וְגוֹרֵם זֶה שֶׁיִּרְבֶּה בְּעֵינָיו וְיַסְפִּיק אֶצְלוֹ מָה שֶׁקָּדַם לוֹ מֵהֶם וְלַחְשֹׁב שֶׁדַּי לוֹ בְּמָה שֶׁיָּצָא לוֹ מִן הַשֵּׁם הַטּוֹב וְהַשֶּׁבַח אֵצֶל בְּנֵי אָדָם וְלִבְזוֹת בְּנֵי אָדָם וְלִגְעֹל אוֹתָם וּלְסַפֵּר בִּגְנוּתָם וְלִהְיוֹת חַכְמֵי דּוֹרוֹ וּגְדוֹלֵיהֶם פְּחוּתִים בְּעֵינָיו וּלְהִתְפָּאֵר בְּקִצּוּר חֲבֵרָיו וְסִכְלוּתָם וְזֶה הוּא הַנִּקְרָא אֵצֶל רז״ל מִתְכַּבֵּד בִּקְלוֹן חֲבֵרוֹ וּבְזֶה לֹא יִהְיֶה נִכְנָע וְלֹא עָנָיו.
The reprehensible one - that a person prides himself on his wisdom or a righteous man on his good deeds. This causes the wisdom and righteousness to become magnified in his eyes, so that he is satisfied with what he has already accomplished, and thinks that it is enough for him the good reputation and praise he has achieved from his fellow men. This will cause him to look down on others, despise them, and speak badly of them, to belittle the wise men of his generation in his eyes, and glorify himself in the shortcomings and ignorance of other people. Our Rabbis of blessed memory call this: "one who seeks honor by putting down others (has no share in the world to come)". One like this will never be submitted nor humble.
וְהַמְּשֻׁבָּח כְּשֶׁמִּתְגָּאֶה הֶחָכָם בְּחָכְמָתוֹ וְהַצַּדִּיק בְּמַעֲשֵׂהוּ הוֹדָאָה לְגֹדֶל טוֹבַת הַבּוֹרֵא עָלָיו בָּהֶם וְשִׂמְחָה בַּעֲבוּרָם וְיִגְרֹם לוֹ לְהוֹסִיף וּלְהִשְׁתַּדֵּל בָּהֶם וּלְהִכָּנַע לִקְרוֹבָיו וְלִשְׂמֹחַ בַּחֲבֵרָיו וְלָחוּס עַל כְּבוֹדָם וּלְכַסּוֹת סִכְלוּתָם וּלְדַבֵּר בְּשִׁבְחָם וְלֶאֱהֹב אוֹתָם וּלְהָלִיץ בַּעֲדָם וּלְהִזָּהֵר בִּכְבוֹדָם וְיִמְעֲטוּ בְּעֵינָיו כָּל מַעֲשָׂיו הַטּוֹבִים, תָּמִיד טוֹרֵחַ לְהַרְבּוֹת מֵהֶם, נִכְנָע בַּעֲבוּר חֲלִישׁוּתוֹ מֵהַשִּׂיג מַאֲוַיָּיו בָּהֶם, מַשְׁפִּיל עַצְמוֹ לְמִי שֶׁמְּקַוֶּה תּוֹסֶפֶת עַל יָדָיו, מוֹדֶה לֵאלֹהִים עַל מָה שֶׁחֲנָנוֹ מִן הַמַּעֲלוֹת וּמְשַׁבֵּחַ אוֹתוֹ עַל אֲשֶׁר הֱפִיקוֹ לִקְנוֹת הַחֲמוּדוֹת.
The praiseworthy one - the pride of the wise man in his wisdom or of the righteous man in his good deeds when it is an expression of his gratitude to the Creator for helping him greatly on them, and of his joy in them. When it causes him to improve and continue exerting himself in them, and to be humble to his colleagues, happy with their success, and concerned for their honor. To not reveal their failings and to speak good of them. To love them and judge them favorably, and to be careful of their honor. All of his own good deeds will seem few in his eyes, and he will always exert himself to increase them. He will be humbled by his inability to reach his longing in them. He will lower himself before someone who he hopes will help him to increase in them. He will be grateful to G-d for having graced him with qualities and thanks Him for helping him to reach exalted levels.
וְזֹאת הַגַּאֲוָה אֵינָהּ מַזֶּקֶת לַכְּנִיעָה וְלֹא מַרְחֶקֶת אוֹתָהּ וּבְכָמוֹהָ אָמַר הַכָּתוּב (דה״ב יז) וַיִּגְבַּהּ לִבּוֹ בְּדַרְכֵי ה׳ אַךְ הִיא מְסַיַּעַת אוֹתָהּ וּמוֹסִיפָה בָּהּ כמ״ש (משלי כב) עֵקֶב עֲנָוָה יִרְאַת ה׳:
This kind of arrogance (aggrandizing) is not detrimental to submission and does not repel it. The verse says of Yehoshafat "And his heart was uplifted in the ways of the L-ord" (Divrei Hayamim II 17:6), just the opposite - such pride helps humility and increases his submission as written "In the wake of humility comes fear of the L-ord, riches, honor, and life" (Mishlei 22:4).