What did Pharaoh mean when he said, "Ki Osah Atem Mevakshim"?
Rashi and Rashbam: He meant that Moshe had asked for permission to sacrifice to his G-d, and it was not the done thing for children (and women - Rashbam) to sacrifice.
Oznayim la'Torah: He meant that actually, he was concerned that the Jewish men should not die either, but what could he do? They insisted on going out in spite of the dangers involved - at their own peril.
Why did Pharaoh suddenly confine his permission to leave to the men - which he did not do in the previous Pasuk?
Oznayim la'Torah: Because he immediately regretted having given permission for the women to leave - when he remembered that the Jewish women would make good husbands for the Egyptian men. 1
Pharaoh did not understand that, when sacrificing to Hashem, one rejoices and participates by eating part of the Korban that one is sacrificing. 2 Consequently, he argued, there was no point in allowing the women and children to go and sacrifice - seeing they would not participate in the sacrificing of the animals anyway. 3
Oznayim la'Torah: Similar to his statement in Parshas Shemos, "v'Chol ha'Bas Techayun" (1:23).
Indeed, that is why Nochrim may only sacrifice Olos - but not Shelamim.
This also explains, a. the discussion that the Torah describes in 10:24-25 - where Pharaoh agreed to let the people go and serve Hashem (who needs sacrifices?); and Moshe retorted "Gam Atah Titen b'Yadeinu Zevachim v'Olos" - Olos, to offer to Hashem, and Zevachim, to eat - since eating the Korban constitutes an integral part of the Avodah; b. Why did Moshe say above, "Ki Chag Hashem Lanu!" (10:9) - with reference to an affair that is celebrated with joy and where everyone participates ('Chag" generally refers to the Korban Chagigah, which is eaten by the owner). See Oznayim la'Torah to 10:10, DH 'Ki Chag Hashem Lanu.'
Why does the Torah omit the name of the one who expelled them?
Why did Moshe and Aharon wait until Pharaoh had them driven out?
Riva (in Tosfos ha'Shalem 5): Because, since Pharaoh sent to return them to him, they did not want to leave without his permission.
Oznayim la'Torah: They were waiting for Pharaoh to discuss the issue with his advisors. 1
See Oznayim la'Torah.
QUESTIONS ON RASHI
Rashi writes: "'Not so!' - [It shall not be] as you said, to bring the children with you!" What is Rashi clarifying?
Gur Aryeh: The exclamation "not so!" isn't referring to the preceding Pasuk ("... May G-d be with you when I send you out with your children!" - 10:10). Pharaoh of course meant that there is no way that he would do so, such that he was cursing them (that Hashem should not be with them) - and Pharaoh was not retracting his words. Rather, "not so" refers back to 10:9; meaning, 'the children shall not accompany you.'
Rashi writes: "'For that is what you are requesting' - I.e., that is what you have requested until now." What is Rashi clarifying?
Gur Aryeh: Although the verse is in present tense (Mevakshim), this is difficult, for Moshe was actually requesting now that the children should go along. Rashi therefore translates it in the past tense (Bikashtem) - 'Based on your previous requests to go and sacrifice in the wilderness, what you were asking for then, is that only the men should go.'
Rashi writes: "'And he chased them away' - This is an abbreviated expression; it does not explain who did the chasing." But perhaps it refers to Pharaoh himself (who has been the subject, since he began speaking in 10:8)?
Gur Aryeh: The verse will mention Pharaoh below, "... he chased them away from before the presence of Pharaoh." This means that the chaser was someone else.