Several answers have been suggested to explain the end of 25:19. Rashi (on 25:19, based on Baba Metzia 87a) explains that the end of the verse is to stress that Yitzhak was Avraham’s son since he looked like Avraham, and not Avimelekh’s son as claimed by cynics. Ibn Ezra (on 25:19) quotes this idea and adds that maybe the point of the verse is to tell us that Avraham raised Yitzhak. Ramban (on 25:19) suggests that the end of the verse is telling us that only Yitzhak and not Avraham’s other children should be considered Avraham’s successor.
While all of these suggestions are possible, my guess is that the phrase, “Avraham begot Yitzhak,” is recorded as part of the elleh toledot structure of the book of Bereshit, see above our discussion "Introduction: The structure of the book of Bereshit" https://lobashamayim.blogspot.com/2009/10/structure-of-book-of-bereshit.html
Verse 25:19 is an example of a verse that begins a lengthy elleh toledot narrative section of the book of Bereshit, as does 11:27 and 37:2. 25:19 records elleh toledot of Yitzhak, and the section proceeds to recount the story of Yitzhak’s son, Yaakov. This is also the pattern of 11:27, which records the phrase elleh toledot Terah and the ensuing section recounts the story of Terah’s son, Avraham, and 37:2, which record the phrase elleh toledot Yaakov and the ensuing section recounts the story of Yaakov’s son, Yosef.
Even when the phrase elleh toledot begins a lengthy narrative section, still the section is framed from a genealogical perspective. Thus, the lengthy narrative elleh toledot sections begin with a genealogical reference to of a child or children of the person referred to in the heading, and end with the death of the child. For example, 11:27 records elleh toledot Terah, and then records that Terah begot Avram, Nahor and Haran, and fourteen chapters later, the section ends with Avraham’s death, 25:8-11. 37:2 records elleh toledot Yaakov and that Yosef was 17 years old, and the section ends with Yosef’s death, 50:26.
Our elleh toledot section, also begins with genealogical details. It mentions that Yitzhak was the son of Avraham (the first half of 25:19) and then it records the birth of Yitzhak’s children, 25:20-26. The statement that Yitzhak was Avraham’s son, which is known from 21:2,3, was because this was a new toledot section, and genealogical information is repeated in a new toledot section, as for example by Noah’s sons 5:32 and 6:10 and by Terah’s sons 11:26,27. However, in contrast to the other lengthy toledot sections, this elleh toledot section ends with the death of Yitzhak, 35:28,29, and not with the deaths of Yitzhak’s children, Yaakov or Esav. I believe that this anomaly explains the need for the phrase “Avraham begot Yitzhak” in the second half of 25:19.
The elleh toledot section of Yitzhak should have ended with the death of Yaakov following the usual pattern in Bereshit that the section ends with the death of son of the person referred in the elleh toledot phrase. However, Yaakov could not die at the end of the section of elleh toledot Yitzhak since he also plays a crucial part in the story of Yosef, the following section. Accordingly, somebody else had to die at the end of the toledot section to maintain the genealogical framework of the elleh toledot structure, and this person was Yitzhak. Yet, if Yitzhak’s death ended the section, then the section has to start with his birth. Thus, the phrase, “Avraham begot Yitzhak,” is recorded in 25:19 to mark Yitzhak’s birth, which enables his death to end the section.
If the toledot section starts with Yitzhak’s birth and ends with his death, then why was the section not titled elleh toledot Avraham? This would follow the rule that the death of the person who ends the toledot section is the son of the person in the phrase elleh toledot. The answer is that the son of the person in the phrase elleh toledot is also the main character of the section, and Yitzhak is not the main character of the section from 25:19-35:29, as Yaakov is the main character of the section. Therefore, the section begins elleh toledot Yitzhak, which means the main character in the section will be Yitzhak's son, Yaakov, but as Yitzhak’s death ends the section, his birth also begins the section, which is the phrase, “Avraham begot Yitzhak.” Yitzhak’s birth and death are then the genealogical markers to this elleh toledot section from 25:19 through 35:29.
Even when the phrase elleh toledot begins a lengthy narrative section, still the section is framed from a genealogical perspective. Thus, the lengthy narrative elleh toledot sections begin with a genealogical reference to of a child or children of the person referred to in the heading, and end with the death of the child. For example, 11:27 records elleh toledot Terah, and then records that Terah begot Avram, Nahor and Haran, and fourteen chapters later, the section ends with Avraham’s death, 25:8-11. 37:2 records elleh toledot Yaakov and that Yosef was 17 years old, and the section ends with Yosef’s death, 50:26.
Our elleh toledot section, also begins with genealogical details. It mentions that Yitzhak was the son of Avraham (the first half of 25:19) and then it records the birth of Yitzhak’s children, 25:20-26. The statement that Yitzhak was Avraham’s son, which is known from 21:2,3, was because this was a new toledot section, and genealogical information is repeated in a new toledot section, as for example by Noah’s sons 5:32 and 6:10 and by Terah’s sons 11:26,27. However, in contrast to the other lengthy toledot sections, this elleh toledot section ends with the death of Yitzhak, 35:28,29, and not with the deaths of Yitzhak’s children, Yaakov or Esav. I believe that this anomaly explains the need for the phrase “Avraham begot Yitzhak” in the second half of 25:19.
The elleh toledot section of Yitzhak should have ended with the death of Yaakov following the usual pattern in Bereshit that the section ends with the death of son of the person referred in the elleh toledot phrase. However, Yaakov could not die at the end of the section of elleh toledot Yitzhak since he also plays a crucial part in the story of Yosef, the following section. Accordingly, somebody else had to die at the end of the toledot section to maintain the genealogical framework of the elleh toledot structure, and this person was Yitzhak. Yet, if Yitzhak’s death ended the section, then the section has to start with his birth. Thus, the phrase, “Avraham begot Yitzhak,” is recorded in 25:19 to mark Yitzhak’s birth, which enables his death to end the section.
If the toledot section starts with Yitzhak’s birth and ends with his death, then why was the section not titled elleh toledot Avraham? This would follow the rule that the death of the person who ends the toledot section is the son of the person in the phrase elleh toledot. The answer is that the son of the person in the phrase elleh toledot is also the main character of the section, and Yitzhak is not the main character of the section from 25:19-35:29, as Yaakov is the main character of the section. Therefore, the section begins elleh toledot Yitzhak, which means the main character in the section will be Yitzhak's son, Yaakov, but as Yitzhak’s death ends the section, his birth also begins the section, which is the phrase, “Avraham begot Yitzhak.” Yitzhak’s birth and death are then the genealogical markers to this elleh toledot section from 25:19 through 35:29.