Although at first glance, the act of standing by a wife when her husband is called up for an aliyah to the Torah appears to be similar to that of a child or student standing before their parent or teacher out of respect, it is actually coming from a completely different place. And to clarify, this has nothing to do with the subject of mutual respect which exists naturally and normally between a husband and wife.
To understand the concept generally, requires first mentioning one of the details of a common practice by many Jews. Namely the recital of the six remembrances said each day. The second of those is what is stated in Devarim 4:9-10 which says:
רַ֡ק הִשָּׁ֣מֶר לְךָ֩ וּשְׁמֹ֨ר נַפְשְׁךָ֜ מְאֹ֗ד פֶּן־תִּשְׁכַּ֨ח אֶת־הַדְּבָרִ֜ים אֲשֶׁר־רָא֣וּ עֵינֶ֗יךָ וּפֶן־יָס֙וּרוּ֙ מִלְּבָ֣בְךָ֔ כֹּ֖ל י֗וֹם אֲשֶׁ֨ר עָמַ֜דְתָּ לִפְנֵ֨י יְהוָ֣ה אֱלֹהֶיךָ֮ בְּחֹרֵב֒ בֶּאֱמֹ֨ר יְהוָ֜ה אֵלַ֗י הַקְהֶל־לִי֙ אֶת־הָעָ֔ם וְאַשְׁמִעֵ֖ם אֶת־דְּבָרָ֑י אֲשֶׁ֨ר יִלְמְד֜וּן לְיִרְאָ֣ה אֹתִ֗י כָּל־הַיָּמִים֙ אֲשֶׁ֨ר הֵ֤ם חַיִּים֙ עַל־הָ֣אֲדָמָ֔ה וְאֶת־בְּנֵיהֶ֖ם יְלַמֵּדֽוּן׃ יְמֵ֣י חַיֶּ֑יךָ וְהוֹדַעְתָּ֥ם לְבָנֶ֖יךָ וְלִבְנֵ֥י בָנֶֽיךָ׃
But take utmost care and watch yourselves scrupulously, so that you do
not forget the things that you saw with your own eyes and so that they
do not fade from your mind as long as you live. And make them known to
your children and to your children’s children: The day you stood before the L-RD your G-d at Horeb, when the L-RD said to Me, “Gather the people to Me that I may let them hear My words, in order that they may learn to revere Me as long as they live on earth, and may so teach their children.”
To emphasize, this is stated as a negative command (הִשָּׁ֣מֶר לְךָ֩ וּשְׁמֹ֨ר נַפְשְׁךָ֜ מְאֹ֗ד פֶּן־תִּשְׁכַּ֨ח) and women, like men, are obligated in all the negative commandments.
Many of the practices which we have are essentially recreating and replaying what took place, what is described in various parts of the Torah.
When we are called up for an aliyah to the Torah, whether during the week, and even more so on Shabbat, the day of the week that the Torah was actually given, we are replaying what actually took place at Matan Torah.
When a husband is called up to the Torah, it is completely consistent with what the Torah teaches and a good practice that his wife, if present, would also stand. That is because generally speaking, husband and wife are viewed in the Torah as one individual, two parts of one being, like it says in Bereshit 2:23-24.
וַיֹּאמֶר֮ הָֽאָדָם֒ זֹ֣את הַפַּ֗עַם עֶ֚צֶם מֵֽעֲצָמַ֔י וּבָשָׂ֖ר מִבְּשָׂרִ֑י לְזֹאת֙ יִקָּרֵ֣א אִשָּׁ֔ה כִּ֥י מֵאִ֖ישׁ לֻֽקֳחָה־זֹּֽאת׃
עַל־כֵּן֙ יַֽעֲזָב־אִ֔ישׁ אֶת־אָבִ֖יו וְאֶת־אִמּ֑וֹ וְדָבַ֣ק בְּאִשְׁתּ֔וֹ וְהָי֖וּ לְבָשָׂ֥ר אֶחָֽד׃
Then the man said, “This one at last Is bone of my bones And flesh of my flesh. This one shall be called Wife, For from man was she taken.”
Hence a man leaves his father and mother and clings to his wife, so that they become one flesh.
But then the logical question that follows this is, if so, why doesn't the wife actually ascend the Bimah?
But this is to fulfill in a complete way what the Torah recounts in Shemot 20:15-16, which says:
וְכָל־הָעָם֩ רֹאִ֨ים אֶת־הַקּוֹלֹ֜ת וְאֶת־הַלַּפִּידִ֗ם וְאֵת֙ ק֣וֹל הַשֹּׁפָ֔ר וְאֶת־הָהָ֖ר עָשֵׁ֑ן וַיַּ֤רְא הָעָם֙ וַיָּנֻ֔עוּ וַיַּֽעַמְד֖וּ מֵֽרָחֹֽק׃
וַיֹּֽאמְרוּ֙ אֶל־מֹשֶׁ֔ה דַּבֵּר־אַתָּ֥ה עִמָּ֖נוּ וְנִשְׁמָ֑עָה וְאַל־יְדַבֵּ֥ר עִמָּ֛נוּ אֱלֹהִ֖ים פֶּן־נָמֽוּת׃
All the people witnessed the thunder and lightning, the blare of the horn and the mountain smoking; and when the people saw it, they fell back and stood at a distance.
“You speak to us,” they said to Moses, “and we will listen; but let not God speak to us, lest we die.”
וְכָל־הָעָם֩ (All the people) is also referring to the complete person, meaning in the case of husband and wife, the wife.
And just as it indicates in the written Torah, the wife stands and listens from a distance while her husband, like Moshe Rabbeinu, approaches and ascends.