Escaping the Famine: Did Avraham Sin?

Not long after he arrived in Canaan, Avraham was forced to make a critical decision. He had uprooted his entire family from Charan and moved to Canaan because Hashem had commanded him to do so, but a famine had struck his new homeland (Breishit 12:10). Without the food and water he and his family needed to survive, what was Avraham to do? The Ramban (12:10) writes,

יציאתו מן הארץ, שנצטווה עליה בתחילה, מפני הרעב, עון אשר חטא, כי האלהים ברעב יפדנו ממות. ועל המעשה הזה נגזר על זרעו הגלות בארץ מצרים ביד פרעה
His leaving the Land, about which he was commanded to settle because of the famine, was a sin, for God, in times of famine, saves people from death. And because of this, the exile in Egypt was decreed on his offspring

According to Ramban, Avraham should have had faith in Hashem that He would provide for him during the tough times of the famine; just like Avraham had faith in Hashem that things would work out if he moved from Charan to Canaan, so too he should have had faith and remained in Canaan. His sin was so egregious that Hashem decreed that Avraham's children would suffer as a result and be exiled to the very Egypt that Avraham had runaway to.
Rabbi Don Isaac Abrabanel, vehemently disagrees with the Ramban's theory. He writes,

וכבר ראית דברי הרמב"ן...וכבר תפשו על הדעת הזה הר"ן כי הנה יציאתו מארץ כנען לארץ מצרים מפני הרעב חז"ל מנוהו מכלל הנסיונות ובידוע שה' צדיק יבחן ומי שיעמוד בנסיונו אין ראוי שיקרא חוטא וחליל שינסה השם את אברהם להכשילו...ודי שנאמר עתה ששתי הסבות הניעו לאברהם לרדת למצרים. האחת היא שחשב שהמצוה האלהית היתה לשבת בארץ כנען ושלא נאסר עליו מפני זה ללכת מצרים אם לסחורה או לצורך אחר כי לא היה עובר בזה על המצוה כיון שלא היה דעתו בהליכתו להתישב שמה דירת קבע אלא דירת עראי וימים אחדים עד עבור הרעב ומיד ישוב לארץ כנען וכמו שהיו עושים בני ישראל בהיותם בארץ שהיו הולכים למצרים לעשות סחורה ושבים ובזה האופן היו מעשיו של אברהם לשם שמים... וכבר זכרה התורה הסבה הזאת באמרה וירד אברם מצרים לגור שם כי היה הרעב בארץ רוצה לומר בדרך גרות לא להתישב שם. והסבה הב' היא שהמצוות האלהיות הם על תנאי אשר יעשה אותם האדם וחי בהם ולא שימות בהם
And I have already seen the words of the Ramban...Rabbeinu Nissim has already challenged this position because Avraham left the Land of Canaan for Egypt because of the famine. Furthermore our sages enumerated this as one of the tests given to Avraham and it is known that Hashem only tests the righteous and those who can stand up to his tests. It is suitable to explain that Avraham had two motives for going down to Egypt. Firstly he believed that the divine commandment was to settle in the Land of Canaan; travel to foreign countries such as Egypt for business or some other need was not forbidden. He did not violate the commandment because he did not travel there to settle, but rather he went there temporarily until the famine ended - and when it did, he immediately returned. This is what Bnei Yisrael did when they eventually settled the Land - they went to Egypt to conduct business and then returned home. In a similar vein, Avraham's actions were for the sake of Heaven. And the Torah already alludes to this fact when it says, 'Avraham went down to Egypt to dwell their because there was a famine in the land.' This means to say, he went as a stranger, not to settle. And the second reason he went to Egypt is because God's commandments are conditional - one does not need to give up their life in order to fulfill them.

Rabbi Abrabanel argues with the Ramban and claims that Avraham's actions could not have been a sin because if his acts were sinful, he would have failed one of the tests given to him by God. Furthermore, there was no sin in going to Egypt temporarily. Finally, he went to Egypt because had he stayed in Canaan he would have had to do so at the risk of his life and the lives of his family members. Hashem had commanded him to settle and live in Canaan, not to die there of starvation.