(ז) כל מצות הבן על האב אנשים חיבין ונשים פטורות, וכל מצות האב על הבן אחד אנשים ואחד נשים חיבין, וכל מצות עשה שהזמן גרמה אנשים חיבין ונשים פטורות...
(7) [With regard to] all commandments of the son which are [incumbent] upon the father, men are obligated, and women are exempt. And [with regard to] all commandments of the father which are [incumbent] upon the son, both men and women are obligated. And [with regard to] every positive commandment that is time-dependent, men are obligated and women are exempt...
ת"ר איזוהי מצות עשה שהזמן גרמא סוכה ולולב שופר וציצית ותפילין ואיזוהי מצות עשה שלא הזמן גרמא מזוזה מעקה אבידה ושילוח הקן וכללא הוא הרי מצה שמחה הקהל דמצות עשה שהזמן גרמא ונשים חייבות ותו והרי תלמוד תורה פריה ורביה ופדיון הבן דלאו מצות עשה שהזמן גרמא הוא ונשים פטורות אמר רבי יוחנן אין למדין מן הכללות ואפילו במקום שנאמר בו חוץ
Why does it matter if women are exempt?
דאמר ר' חנינא גדול המצווה ועושה ממי שאינו מצווה ועושה
That R' Chanina stated: Greater is the one who is commanded and does than one who is not commanded and does.
חרש שוטה וקטן אין מוציאין את הרבים ידי חובתן. זה הכלל: כל שאינו מחויב בדבר, אינו מוציא את הרבים ידי חובתן.
A deaf-mute person, or a shoteh [insane person], or a minor, cannot relieve others from their obligation [of hearing the shofar]. This is the general rule: all those who are not obligated to carry out a particular action, cannot release others from their obligation.
Common/answers as to why women are exempt:
David b. Joseph Abudarham (fl. 1340) excerpt from Perush Hatefillot Vehaberakhot
The reason women are exempt from time-triggered positive commandments is that a woman is subjugated to her husband for the fulfillment of his needs. If she were obligated to perform time-triggered commandments, it might happen that just when she is performing the commandment her husband will command her to do his bidding. If she were to fulfill the command of the Creator and ignore his [her husband's] command, woe to her from her husband! And if she were to fulfill his command and ignore that of the Creator, woe to her from her Maker! Therefore the Creator exempted her from his commandments, so that she can be at peace with her husband.

נשים ועבדים וקטנים פטורין מקריאת שמע ומן התפלין, וחיבין בתפלה ובמזוזה ובברכת המזון.
Women, slaves, and minors are exempt from reciting Shema and from tefillin and are obligated in [reciting] Shemoneh Esrei and in [affixing a] Mezuzah and in [reciting] Birkat HaMazon.
Samson Raphael Hirsch (1808-1888) commentary to Lev 23:43
But it seems to us to be rather much more likely that the Torah did not impose these mizvot on women because it did not consider them necessary to be demanded from women. All mizvot shehazman geraman are meant, by symbolic procedures, to bring certain facts, principles, ideas, and resolutions, afresh to our minds from time to time to spur us on afresh and to fortify us to realize them to keep them. God's Torah takes it for granted that our women have greater fervour and more faithful enthusiasm for their God-serving calling, and that this calling runs less danger in their case than in that of men from the temptations which occur in the course of business and professional life. Accordingly it does not find it necessary to give women these repeated spurring reminders to remain true to their calling, and warnings against weaknesses in their business life.
האיש קודם לאשה להחיות ולהשיב אבדה, והאשה קודמת לאיש לכסות ולהוציאה מבית השבי. בזמן ששניהם עומדים לקלקלה, האיש קודם לאשה.
A man supersedes a woman to keep alive and to return a lost object. A woman supersedes a man to clothe and to free from captivity. If they both stand to be disgraced, the man supersedes the woman.
היה ר"מ אומר חייב אדם לברך שלש ברכות בכל יום אלו הן שעשאני ישראל שלא עשאני אשה שלא עשאני בור רב אחא בר יעקב שמעיה לבריה דהוה קא מברך שלא עשאני בור אמר ליה כולי האי נמי אמר ליה ואלא מאי מברך שלא עשאני עבד היינו אשה עבד זיל טפי.
R' Meir used to say: "A man is obligated to recite three blessings every day, and they are the following: ...Who has made me a Jew; ...Who has not made me a woman; ... who has not made me a slave" Rav Acha Bar Yaakov heard his son reciting the blessing of "...who has not made me a slave." He said to him "Is it proper to recite blessings to this extent?" He (his son) said to him "Then what blessing should one recite instead?" He replied: "Who has not made me a slave" But isn't [a slave] the same as a woman? [i.e. why do we need a separate blessing?] A slave is even lower in status.
כל מצוה שהאשה חייבת בה עבד חייב בה כל מצוה שאין האשה חייבת בה אין העבד חייב בה
Every commandment a woman is obligated in, a slave is obligated in, and every commandment a woman is not obligated in, a slave is not obligated in.
(ט) וְהָיָה֩ לְךָ֨ לְא֜וֹת עַל־יָדְךָ֗ וּלְזִכָּרוֹן֙ בֵּ֣ין עֵינֶ֔יךָ לְמַ֗עַן תִּהְיֶ֛ה תּוֹרַ֥ת יְהוָ֖ה בְּפִ֑יךָ כִּ֚י בְּיָ֣ד חֲזָקָ֔ה הוֹצִֽאֲךָ֥ יְהֹוָ֖ה מִמִּצְרָֽיִם׃
(9) And it shall be for a sign unto thee upon thy hand, and for a memorial between thine eyes, that the law of the LORD may be in thy mouth; for with a strong hand hath the LORD brought thee out of Egypt.
Mekhilta de Rabbi Shimon bar Yochai
“That the Torah of the Lord may be in your mouth"— to exclude women [from tefillin]. What is exemplary about tefillin? They are a positive time-triggered commandment from which women are exempt. So, too, are women exempt from all positive time-triggered commandments”
(ו) וְהָי֞וּ הַדְּבָרִ֣ים הָאֵ֗לֶּה אֲשֶׁ֨ר אָנֹכִ֧י מְצַוְּךָ֛ הַיּ֖וֹם עַל־לְבָבֶֽךָ׃ (ז) וְשִׁנַּנְתָּ֣ם לְבָנֶ֔יךָ וְדִבַּרְתָּ֖ בָּ֑ם בְּשִׁבְתְּךָ֤ בְּבֵיתֶ֙ךָ֙ וּבְלֶכְתְּךָ֣ בַדֶּ֔רֶךְ וּֽבְשָׁכְבְּךָ֖ וּבְקוּמֶֽךָ׃ (ח) וּקְשַׁרְתָּ֥ם לְא֖וֹת עַל־יָדֶ֑ךָ וְהָי֥וּ לְטֹטָפֹ֖ת בֵּ֥ין עֵינֶֽיךָ׃ (ט) וּכְתַבְתָּ֛ם עַל־מְזוּזֹ֥ת בֵּיתֶ֖ךָ וּבִשְׁעָרֶֽיךָ׃ (ס)
(6) And these words, which I command thee this day, shall be upon thy heart; (7) and thou shalt teach them diligently unto thy children, and shalt talk of them when thou sittest in thy house, and when thou walkest by the way, and when thou liest down, and when thou risest up. (8) And thou shalt bind them for a sign upon thy hand, and they shall be for frontlets between thine eyes. (9) And thou shalt write them upon the door-posts of thy house, and upon thy gates.
מנלן גמר מתפילין מה תפילין נשים פטורות אף כל מצות עשה שהזמן גרמא נשים פטורות ותפילין גמר לה מתלמוד תורה מה תלמוד תורה נשים פטורות אף תפילין נשים פטורות
From where do we know this? We derive it from Tefillin. Just like by Tefillin women are exempt, so to by all time dependant positive commandments women are exempt. And Tefillin is derived from [the adjacent commandment of] learning Torah. Just like by [the commandment of] learning Torah women are exempt, so too by Tefillin women are exempt.
ר' אליעזר אומר כל המלמד את בתו תורה מלמדה תיפלות
R' Eliezer said: anyone who teaches his daughter Torah, teaches her lewdness.

