why Sarah became the superior prophet to Avraham

1) A fantastic Meshech Chochma on last weeks parsha:

Meshech Chochma points out that when the malach appears to Hagar to tell her that Yishmael will live, he calls to her from the heavens:  וַיִּקְרָא֩ מַלְאַ֨ךְ אֱלֹקים ׀ אֶל־הָגָר֙ מִן־הַשָּׁמַ֔יִם (21:17).  However, in Lech Lecha, when Hagar was first driven out by Sarah, a malach appears and speaks to her directly, not just as a voice echoing from the sky:  וַֽיִּמְצָאָ֞הּ מַלְאַ֧ךְ הֹ׳ עַל־עֵ֥ין הַמַּ֖יִם בַּמִּדְבָּ֑ר עַל־הָעַ֖יִן בְּדֶ֥רֶךְ שֽׁוּר  וַיֹּאמַ֗ר הָגָ֞ר שִׁפְחַ֥ת שָׂרַ֛י אֵֽי־מִזֶּ֥ה בָ֖את וְאָ֣נָה תֵלֵ֑כִי (16:7-8)  Apparently Hagar had somewhat of a spiritual downfall from the time she was first driven from Avraham's house and was no longer worthy of having that direct form of conversation with angels appearing on her level, only of hearing the voice echoing from above.

But don't we find that after the akeidah Avraham too was addressed by a malach that only called to him from the heavens,  וַיִּקְרָ֛א מַלְאַ֥ךְ הֹ׳ אֶל־אַבְרָהָ֑ם שֵׁנִ֖ית מִן־הַשָּׁמָֽיִם!?

Answers the Meshech Chochma: when performing the akeidah Avraham was like the kohen gadol entering the kodesh kodashim on Y"K.  At that moment, no one can be present in the Kd"k, not even an angel.  The angel called to Avraham from the heavens not because Avraham was not worthy of seeing him directly, but aderaba, because the angel was unworthy of being in that holy place where the akeidah occurred.

2) I think my wife'e favorite pasuk in Braishis may be כֹּל֩ אֲשֶׁ֨ר תֹּאמַ֥ר אֵלֶ֛יךָ שָׂרָ֖ה שְׁמַ֣ע בְּקֹלָ֑הּ (21:12) : )  Rashi comments: למדנו שהיה אברהם טפל לשרה בנביאות  Sarah was able to see things that Avraham could not, and therefore he was told to listen to her.

Of course Sarah is one of our great Imahos, but Avraham was not lacking in greatness either, so how is it that he did not measure up to Sarah's prophetic ability?  

Earlier in the parsha, G-d decided to reveals to Avraham what will his plan is for Sdom (18:17-19:

 וַֽהֹ׳ אָמָ֑ר הַֽמְכַסֶּ֤ה אֲנִי֙ מֵֽאַבְרָהָ֔ם אֲשֶׁ֖ר אֲנִ֥י עֹשֶֽׂה׃

וְאַ֨בְרָהָ֔ם הָי֧וֹ יִֽהְיֶ֛ה לְג֥וֹי גָּד֖וֹל וְעָצ֑וּם וְנִ֨בְרְכוּ־ב֔וֹ כֹּ֖ל גּוֹיֵ֥י הָאָֽרֶץ׃

כִּ֣י יְדַעְתִּ֗יו לְמַ֩עַן֩ אֲשֶׁ֨ר יְצַוֶּ֜ה אֶת־בָּנָ֤יו וְאֶת־בֵּיתוֹ֙ אַחֲרָ֔יו וְשָֽׁמְרוּ֙ דֶּ֣רֶךְ הֹ׳ לַעֲשׂ֥וֹת צְדָקָ֖ה וּמִשְׁפָּ֑ט לְמַ֗עַן הָבִ֤יא הֹ׳ עַל־אַבְרָהָ֔ם אֵ֥ת אֲשֶׁר־דִּבֶּ֖ר עָלָֽיו

Rash is already bothered by the lack of connection between the second statement, the fact that Avraham was involved in passing on his legacy of derech Hashem to his children and grandchildren and followers, and the first statement, Hashem's rhetorical question, "Can I hide from Avraham what I plan to do?"  

Chasam Sofer writes that many prophets, e.g. Yirmiyahu, Yishayahu, etc. were able to prophetically see not just events that would occur in their immediate environment, but they prophesized to the world at large as well, to Mitzrayim, to Ashur, to other nations.  The saw the future of the world as a whole, on a vast, global scale.  Avraham, however, if not for G-d's deliberate effort to reveal it to him, was unaware even of what was in store for the nearby city of Sdom.  Why?  Because Avraham was involved in teaching his children, his followers, about G-d, about monotheism, about the 'derech Hashem.'  According to the Meshech Chochma, this pasuk of  לְמַ֩עַן֩ אֲשֶׁ֨ר יְצַוֶּ֜ה אֶת־בָּנָ֤יו וְאֶת־בֵּיתוֹ֙ אַחֲרָ֔יו וְשָֽׁמְרוּ֙ דֶּ֣רֶךְ הֹ׳ is the source for the mitzvah of chinuch.  You can't spend your time in a meditation, seeking prophetic insights, involved in your own growth, when you have a household to train and educate, when you have an outreach program to run.  A guy out there on a college campus giving classes to the barely religious and trying to pull together meals for them every shabbos and programs for during the week can't be expected to be immersed in every sugya the way someone sitting in beis medrash all day with nothing else on their plate is.  

G-d therefore said that it's not fair here,  הַֽמְכַסֶּ֤ה אֲנִי֙ מֵֽאַבְרָהָ֔ם אֲשֶׁ֖ר אֲנִ֥י עֹשֶֽׂה, that Avraham should be blind to what's coming just because his involvement in other areas of avodas Hashem deprives him of the time or kochos to work on his own personal development, his own prophetic ability.  

The gemara in Nazir (29) tells us  איש חייב לחנך בנו במצות ואין האשה חייבת לחנך את בנה.  A woman is exempt from the mitzvah of chinuch.  For the sake of derush let's not get involved in nitpicking on the details of that sugya -- that's what the words say.  If so, the mission of אֲשֶׁ֨ר יְצַוֶּ֜ה אֶת־בָּנָ֤יו וְאֶת־בֵּיתוֹ֙ אַחֲרָ֔יו was perhaps Avraham's mission, but not Sarah's.  Undoubtedly she would have helped him, but it was his primary role, not hers.  

Therefore, perhaps Sarah had more time to herself, to develop her gift of prophecy, in ways that exceeded Avraham's ability.