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 pray, so that she should not die out of distress. 3
Tosfos ha'Shalem (4), Ramban #2: To be sure, Yakov prayed 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 pray 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.
Ohr ha'Chayim #1: He was angry because she cursed herself. Such words of a Tzadik take effect. 6
Ohr ha'Chayim #2: She said 'give to me children', and not 'pray for me.'
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).
Ramban: 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 boor interrupts another's words, but a Chacham does not (Avos 5:7)! Perhaps he did so to stop her from cursing herself or saying heresy (refer to 30:2:1:1,5). (PF)
Why did he reject her argument?
Rashi: He countered that his father prayed because he did not have children yet, whereas he (Yakov) already had children. 1
Ha'Emek Davar: She thought that Bnei Leah are not important to him, and it is as if he has no children. This is not so!
The Ramban queries why Yakov would not pray for her, but concedes that Chazal (Bereishis Rabah 71:7) 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