What did Aharon see?
Rashi #1: He saw that the calf contained a spirit of life 1 and that the Satan was succeeding, so he realized that it was not possible to reject their request completely.
Rashi #2 and Targum Yonasan: He saw that they had murdered his nephew Chur, 2 when he tried to stop them and he was afraid 3 that if he followed suit, they would kill him as well.
Rashi #3: He decided that it was preferable that he should be punished for sinning rather than them.
Rashi #4: He realized that if he were to withdraw and allow them to build the Mizbe'ach, one person will bring earth, the other, stones, and they will complete it in no time. Better that he continues to build slowly, slowly; meanwhile, Moshe was bound to return.
Ramban and Moshav Zekenim: He saw that they were bent on doing evil, that their minds were hooked on the calf and realized that, if left to their own devices, they would build many Mizb'chos to the calf. 4
Da'as Zekenim and Hadar Zekenim: He saw that they had erred, and was apprehensive that upon realizing that the calf would not save them, they would appoint a leader. Therefore, he built a Mizbe'ach to delay them until Moshe came.
Sanhedrin, 7a: Refer to 32:5:1:2: He was afraid that if they would kill him they would fulfil the Pasuk in Eichah, 2:20 "Im Yehareg ba'Mikdash Hashem Kohen ve'Navi", a sin which would have no remedy - and it is therefore preferable that he should make for them an Eigel, in which case they wold at least be able to do Teshuvah'
Da'as Zekenim (in Pasuk 4): His entire intention was le'Shem Shamayim (as opposed to one opinion in Sanhedrin 7a - Hadar Zekenim (in Pasuk 3). The Pesukim praise him - "Ki Sifsei Chohen Yishmeru Da'as", "ve'Rabim Heishiv me'Avon" - with reference to Chet ha'Eigel. Had they killed him, there would have been no solution [for Yisrael] - "Im Yehareg be'Mikdash Hashem Kohen ve'Navi". (Vayikra Rabah 10:3 maintains that Aharon received Matnos Kehunah for this. On the other hand, the Pasuk in Eikev Devarim, 9:20 states that Hashem was very angry with Aharon, and wanted to destroy him! It seems that even though he erred, and he was punished for the Chilul Hashem that resulted (Avos 4:4), he was rewarded for his good intention - PF).
Why did Aharon build a Mizbe'ach?
Rashi and Ramban #1: In order to put them off for as long as possible, in the hope that in the meantime, Moshe would return. 1
Ramban #2: In honor of Hashem, so that they should sacrifice on it to Him and not build altars for their idols to their shame.
What did Aharon have in mind when he declared "Chag la'Hashem Machar"?
Rashi: He hoped that in the interim, Moshe's would return with the Luchos and they would celebrate his homecoming with a Yom-Tov, and that they would sacrifice on the Mizbe'ach that he had built, in honor of Hashem.
Seforno: He meant that tomorrow would be a Yom-Tov for Hashem, and that they should not exchange it for another god.
Targum Yonasan: Dejected on account of the rebellion that was taking place, he announced that the next day (when Moshe returned) they would make a Yom-Tov to celebrate the death of the rebels - 'rebels who exchanged the Shechinah for this ox'
Da'as Zekenim and Hadar Zekenim: He meant that they would crown their new leader and make a Yom-Tov in the Name of Hashem and offer Shelamim to Him - like Yisrael did when Sha'ul was crowned. 1
Moshav Zekenim: He meant that tomorrow, Hashem would bring 'Chaga' (destruction) on the heretics.
See Sh'muel 1, 11:15.
