On what grounds was Yakov angry with Rachel?
Rashi, Seforno, Targum Onkelos and Targum Yonasan: Because she intimated that he was able to replace Hashem by granting her children. 1 If she wanted children, then she should turn to Hashem (and not to him), for He was the One who withheld children from her. 2
Tosfos ha'Shalem (4), Ramban #1: He was angry because she expected him to put on sack-cloth and ashes and to fast (out of his love for her) and to Daven, so that she should not die out of distress. 3
Tosfos ha'Shalem (4), Ramban #2: To be sure, Yakov Davened for Rachel, only his Tefilos were not answered. And Rachel now complained that, if his father's Tefilos on behalf of his wife were answered, then he must Daven more, and his Tefilos too will be answered. To which Yakov replied that bearing children was not in his hands, but in the Hands of Hakadosh-Baruch-Hu, and that if his father's Tefilos were answered, it was because he was a Tzadik. Moreover, Yitzchak was destined to have children, whereas he (Yakov) already had children, and it was she from whom Hashem was withholding them. 4
Bechor Shor: He interrupted before she finished speaking. 5 He thought that she asked him to put a fetus in her womb.
Though that was not what she really meant (Seforno).
Since he discerned in her signs that she was an Ailonis (who could not have children).
Women beloved to their husbands often frighten their husbands through possibility of death. Due to his rebuke, she could not rely on him, and prayed for herself.
This is astounding. A Golem interrupts another's words, but a Chacham does not (Avos 5:7)! Perhaps he did so because he thought that she was saying heresy. (PF)
And why did he reject her argument?
Rashi: He countered that his father Davened because he did not have children yet, whereas he (Yakov) already had children. 1
The Ramban queries this and, citing the Midrash, he explains that Chazal took Yakov to task- 'Is that how one answers someone in distress?'
What is the meaning of "ha'Sachas Elokim Anochi"?
Tosfos ha'Shalem (6): Rachel wanted Yakov to change her name so she could have children. 1
Tosfos ha'Shalem (7): We learn from here that Yakov's image is on the Kisei ha'Kavod. 2
רש"י: התחת אלוקים אנכי - וכי במקומו אני: למה לא פירש כפשוטו שהיא תחת רשות ה'?
גור אריה: כל אדם הוא תחת רשותו יתברך [ויעקב לא היה צריך לומר זאת].
רש"י: אשר מנע ממך - את אמרת שאעשה כאבא, אני איני כאבא, אבא לא היו לו בנים אני יש לי בנים, ממך מנע ולא ממני: מנין שכך אמר לה יעקב?
גור אריה: אם לא כן, "ממך" למה לי? [אלא כוונתו- רק ממך מנע ולא ממני].
וכי בגלל שהוא כבר זכה לבנים לא יתפלל עליה?
גור אריה: השבטים אינם כשאר תולדות אלא כוונת ה' להוציא את השבט דווקא מאשה מסויימת, ולכן לא רצה יעקב לשנות את הדבר._
רש"י: אבא לא היו לו בנים אני יש לי בנים: למה שאר האבות היו עקרים ויעקב לא?