Which 'Toldos' (progeny) is the Torah referring to?
Rashi and Ramban: It is referring to Yaakov and Esav, mentioned below. 1
Seforno: "Toldos" means events, and the Sedra is indeed, dedicated to the major events in Yitzchak's life.
Ha'amek Davar: It is his way of life.
Gur Aryeh: What is Rashi clarifying? Yaakov and Esav had not been born yet; their birth is written later on (25: 24-26). Rashi explains that this phrase nevertheless refers to Yaakov and Esav. The intervening verses describe the events leading to their birth.
Why did the Pasuk add, "Avraham Holid Es Yitzchak"?
Rashi #1: To teach us that it was after HaSh-m changed his name to Avraham, that he bore Yitzchak.
Rashi #2 and Targum Yonasan: It did so to counter the mockers, who claimed that Sarah was pregnant from Avimelech. So what did HaSh-m do? He formed Yitzchak's features to resemble 1 Avraham so exactly, that everybody had to admit that 'Avraham bore Yitzchak.' 2
Ibn Ezra: It means that Avraham raised Yitzchak.
Ramban: Since the Torah is about to discuss with the history of Klal Yisrael starting with Yitzchak, it begins by mentioning the illustrious founder of the nation, Avraham. 3
Rashbam, Ramban and Seforno: Refer to 25:12:1:1.
Ohr ha'Chayim #1: Initially, Yitzchak had a female aspect and was unable to father children. Via the Akeidah, Avraham implanted in him male nature and the ability to father.
Ohr ha'Chayim #2: HaSh-m answered Yitzchak, for he was a Tzadik ben Tzadik (Yevamos 64a). Due to Avraham, he merited to have children.
Ohr ha'Chayim #3: Bereishis Rabah (63:2) says that Avraham was saved from Nimrod's furnace in the merit of Yaakov. Due to [Yaakov,] Toldos Yitzchak, Avraham lived, and was able to father Yitzchak.
Ohr ha'Chayim #4: The primary Toldos of Tzadikim are their deeds. Yitzchak resembled Avraham regarding deeds and virtue.
Ohr ha'Chayim #5: Avraham planted in Yitzchak understanding of HaSh-m. Avraham had a harder Avodah; his father served idols, and Avraham needed to find HaSh-m by himself.
Ohr ha'Chayim #6: In one way, Yitzchak was at a higher level than Avraham; he was a Tzadik ben Tzadik.
Ohr ha'Chayim #7: Due to Avraham's merit, Yitzchak did not have afflictions, 4 unlike Avraham. He had only wealth and honor, like the Ramban said.
Malbim: In contrast to Yishmael, who was like the peel and is attributed to his mother, Yitzchak was the primary fruit of Avraham.
Ha'amek Davar: His way of life reflected that he was Avraham's son - unlike Yishmael.
Da'as Zekenim, Hadar Zekenim, Rosh: The Gematriya of Holid is the same as that of Domeh (resembles).
Gur Aryeh: It is not that the Torah itself needs to prove this; rather, it is telling us how Yitzchak was acknowledged even by the public as "son of Avraham." Because they were similar in appearance, everyone testified to this.
Moreover, the Ramban explains, the Torah ought really to have begun with "These are the generations of Avraham;" only it did not do so to avoid having to include Yishmael and the Bnei Keturah. So instead it inserted "Avraham bore Yitzchak."
This is difficult. Yishmael quarreled with him about the inheritance, and shot arrows at him (Perush #2 in Rashi to 21:10), he was childless for 20 years, he needed to relocate due to famine, he feared being killed due to Rivkah, and had to abstain from her for a long time, Pelishtim envied him, quarreled with him and told him to leave, Esav's wives embittered his life, and he became blind! The Ramban discussed only wealth! (PF)
Why does it say here, "Avraham Holid Es Yitzchak," and about Yishmael it says, "Asher Yaldah Hagar" (25:12)?
Hadar Zekenim: The son of a Nochris is not called your son, rather, her son (Kidushin 68b. Only Yitzchak is attributed to Avraham.)
Why didn't the Torah write "Eleh" (without a Vav), to disqualify (exclude) Bnei Keturah and Bnei Yishmael?
Moshav Zekenim: It is because Yishmael did Teshuvah.
QUESTIONS ON RASHI
Rashi writes: "'These are the offspring of Yitzchak' - Yaakov and Esav." Why does the Torah introduce them as Toldos - before they were even born?! (This is unlike other instances of this term in the Torah.)
Gur Aryeh: Yaakov and Esav demonstrated their respective characters even before they were born. Yaakov was righteous and pushed out towards a Beis ha'Keneses, whereas Esav pushed towards the opposite. 1 Therefore, they can already be called "offspring."
See Rashi to 25:22. This means that they were not merely part of their mother (Ubar Yerech Imo); rather, each was already independent and following his own path. (EK)
Rashi writes: "[The verse] had to say, 'Avraham fathered Yitzchak.'" Why doesn't Rashi explain the verse simply, 'These are the events in the life of Yitzchak'?
Gur Aryeh: If 'Toldos Yitzchak' would mean 'events in the life of Yitzchak,' obviously the first event was that he was born! But Rashi interprets 'Toldos' as literally 'children,' i.e. Yaakov and Esav. As such, he must offer a different explanation for the added phrase, "Avraham fathered Yitzchak."
Rashi writes: "Once the verse wrote, 'Yitzchak, son of Avraham,' it had to say, 'Avraham fathered Yitzchak.'" But let it omit both phrases?
Gur Aryeh: The verse associates these children with Avraham, to teach us that HaSh-m granted them in fulfillment of His promise to Avraham, and in his merit. 1 "Ki b'Yitzchak Yikarei Lecha Zara" (21:12) is interpreted, 'Some of Yitzchak's children - but not all' (Nedarim 31a), excluding Esav. 2
Rashi writes: "There is proof that Avraham fathered Yitzchak!" Why is this proof written here, and not earlier, such as at the time of Yitzchak's birth?
Gur Aryeh: Our verse is stating the pedigree of Yitzchak's children, as descendants of Avraham (as in the verse, "Children's splendor is their ancestors" (Mishlei 17:6)). To counteract the words of the scoffers against Yaakov's Yichus, the Torah emphasizes Yitzchak's resemblance to Avraham here. 1
Rav Shimon Schwab: At first, no one paid the scoffers any heed. But when the wicked Esav was born, people wondered how he could have possibly come from Avraham; saying, 'Perhaps Yitzchak's father was Avimelech after all!' To quash these rumors, HaSh-m now changed Yitzchak's appearance to resemble Avraham - only after Esav was born!
Avraham was still alive at the time, and the resemblance was self-evident. (CS).