Parshat Toldot: A Striking Resemblance

Our parsha is filled with drama; Yitzchak and Rivkah struggle with infertility, Yaakov and Esav are born, Yitzchak and Rivkah play favorites with their children, Yaakov convinces Esav to sell him his birthright, famine forces Yitzchak to move his family to Gerar and Yaakov takes Esav's blessing forcing him to flee to Lavan to avoid his brother's wrath.
With the all of the excitement contained within the parsha, one could easily gloss over the first pasuk of the sedra and not notice an apparent redundancy. The pasuk states (Breishit 25:19),

ואלה תולדות יצחק בן אברהם אברהם הוליד את יצחק
And these are the offspring of Yitzchack son of Avraham, Avraham begot Yitzchak.

If Yitzchak is the son of Avraham, of course Avraham begot him; seemingly, the Torah could have done without the final clause of the pasuk!
The Ibn Ezra writes, in an explanation that is most likely the closest to peshat, the simplest understanding, of the pasuk,

ויש אומרים כי טעם הוליד גדל ורבה, כמו יולדו על ברכי יוסף (נ,כג), והעד שאמר וישלחם מעל יצחק בנו
And there are those who say that the meaning of 'begot' is 'raised', like 'they were raised on Yosef's knees'(Breishit 50:23), and the proof is that it says 'he sent them away from Yitzchak his son' (Breishit 25:6)

According to the Ibn Ezra, the first part of the pasuk informs us that Yitzchak was Avraham's son, while the second part tells us that not only was he his son, but he was also raised by him. This second clause is not redundant because Yitzchak is the only one of Avraham's children who was raised by Avraham. All of the others (Yishmael, Zimran, Yakshan, Medan, Midian, Yishbak and Shuach - see Breishit 25:2) were sent away; Yishamel was kicked out of the house with his mother at the urging of Sara and we are told explicitly (25:6) that the other children were sent away to lands in the east.
The following Midrash, quoted by Rashi, paints a completely different picture. Rashi writes,

אברהם הוליד את יצחק - על ידי שכתב הכתוב יצחק בן אברהם הוזקק לומר אברהם הוליד את יצחק, לפי שהיו ליצני הדור אומרים מאבימלך נתעברה שרה, שהרי כמה שנים שהתה עם אברהם ולא נתעברה הימנו, מה עשה הקב"ה, צר קלסתר פניו של יצחק דומה לאברהם, והעידו הכל אברהם הוליד את יצחק, וזהו שכתב כאן יצחק בן אברהם היה, שהרי עדות יש שאברהם הוליד את יצחק:
Since Scripture wrote: 'Yitzchak the son of Avraham,' it had to say: 'Avraham begot Yitzchak,' because the scorners of the generation were saying that Sara had conceived from Avimelech, for she had lived with Avraham for many years and had not conceived from him. What did the Holy One, blessed be He, do? He shaped the features of Yitzchak’s face to resemble Avraham’s, and everyone attested that Avraham had begotten Yitzchak. This is the meaning of what is written here: 'Yitzchak, the son of Avraham,' because here is proof that 'Avraham begot Yitzchak.'

According to Rashi, Sara conceived not long after the incident with Avimelech (Breishit 20). People began to scoff and started rumors that Avimelech was the father of Yitzchak. They began to reason that Avraham and Sara had been married for years and had not been able to have children and after being abducted by Avimelech she suddenly had a child? It must not be Avraham's! In order to dispel this notion, Hashem caused Yitzchak's appearance to starkly resemble Avraham's so that no one could claim that Avimelech was his father.
Rabbi Shlomo Efraim Luntschitz (1550-1619) in his commentary the Kli Yakar has a different take on the Midrash. He writes,

וכדי שלא ימצא המערער מקום לחלוק, ולומר אם יצחק נולד כל כך בקדושה וטהרה א”כ למה יצא ממנו עשו שהיה צד נשים תחת בעליהן, ודאי מאבימלך נתעברה שרה ע”כ נמשך בן אחד אחר טבעה של שרה, והשני אחר טבע אבימלך, כי מטעם זה אמרו רז”ל (ב”מ פז.) שהיה צר קלסתר פניו דומה לאברהם.
In order that the scorner would not find room to argue and say that if Yitzchak was really born with holiness and purity, then how could Esav who hunted women from their husbands have come from him? It must be that Avimelech impregnated Sara. As a result one child (of Yitzchak's) had the nature of Sara and the second one had the nature of Avimelech. It is for this reason that our Rabbis of blessed memory said that Hashem shaped the features of his face to look like Avraham's.

The explanation of Rashi seems to be more rational than that of the Kli Yakar. Rashi intimates that people began to question who Yitzchak's father was around the time he was born and so Hashem quashed those rumors by making Yitzchak look like his father; presumably these changes took place as he matured - it is often hard to tell if babies look like their parents at a young age, but once they get older the resemblances become clearer. According to Rashi, Yitzchak began to resemble his father in a more natural way. However, according to the Kli Yakar people only began to question Yitzchak's lineage once they saw the behavior of his rebellious, amoral, son Esav. The Kli Yakar explains that it was at this point, when Esav attained his less than savory reputation, that God altered Yitzchak's appearance to look like Avraham in order to put to rest all of the rumormongers who claimed Yitzchak could have only been the father of Esav if his father was actually Avimelech; according to the Kli Yakar Yitzchak had a sudden change in physical appearance when he was over 60 years old (Esav was born when Yitzchak was 60 and could have only been recognized as a rebel once he grew up).
Perhaps another lesson can be gleaned from this Kli Yakar. The Kli Yakar wrote that the people began to question the identity of Yitzchak's father once they saw Esav's behavior because they could not believe the grandson of Avraham would behave in such a way. However their hypothesis was disproved when Hashem changed Yitzchak's appearance to make him look like a clone of Avraham. While Hashem dispelled the rumors, the question was never answered - how can it be that Avraham could have a grandson and Yitzchak a son, as evil as Esav? The Kli Yakar never answers the question, but an answer can be found in the following Gemara (Nedarim 81a),

מפני מה אין מצויין ת"ח לצאת ת"ח מבניהן? אמר רב יוסף: שלא יאמרו תורה ירושה היא להם.
Why is it uncommon for Torah scholars to have children whom are also Torah scholars? Rabbi Yosef said: So that they (people) will not say that the Torah is their inheritance

The Gemara observes that Torah scholarship and observance are not dynastic. After all, we hear about many heroes of the Tanach who had children that did not follow in their footsteps (Yishmael, Esav, Moshe's sons, Aharon's sons, the sons of Eli the Kohen Gadol, the sons of Shmuel, many of the sons of David Hamelech, etc.). Rav Yosef answers that the reason why this is such a common occurrence is because Hashem does not want people to think that the Torah is private property, an inheritance passed down from father to son; people should not think that because their parents were not great Torah scholars they do not have a share in Hashem's Torah. Hashem made examples out of certain talmidei chachamim to illustrate this rule. An example of this rule is Esav. How could it be that Avraham had a grandson and Yitzchak a son as wicked as Esav? To teach us that Torah knowledge and leadership are not hereditary. It is within everyone’s grasp - man, woman and child.