Q. Out of the five reasons given for the fast of Shiva Asar Betamuz, the most important seems to be the first one, the day when the luchos were broken, due to the making of the eigel, since that totally changed the history of our nation. Our sages say that if the luchos would not have been broken no other nation could have ruled over us. Therefore there would not have been any persecutions, galut, and churban. Why is it then that the gemara on Rosh Hashanah says that after the first churban they kept the 9 of Tamuz as the fast day and not the 17? Was not the 17 already a far greater day of tragedy and mourning?

A. One of the hardest posukim to understand in Parshas Ki Sissa is Aharon telling the people, “Chag Lashem Mochor,” We are going to celebrate a Yom Tov to Hashem tomorrow. Notwithstanding Rashi’s interpretation that he wanted to gain time so maybe Moishe would return before the eigel was made, why call it Chag L’Hashen; why place Hashem’s name into it? It was not necessary. It was exactly the opposite and it constituted the greatest chilul Hashem.
Based on the Targum Yonosson and also found in Oznaim Latorah is the understanding that since after Moshe Rabbeinu came down, the wrongdoers were punished and filtered out from Klal Yisroel, in that sense it was a Chag Lashem. As the Targum mentions, a sad Chag Lashem.
The Arizal’s interpretation is that it was a reference to the future geulah, when Shiva Asar Betamuz will indeed become a Yom Tov.
In another way there was great redemption and delivery on that day too. When Rabi Yohanan ben Zakai met with Vespasian, Medresh (Eicha Rabba 1, See Gittin 56b), mentions that he asked to be granted that when the city falls, the Romans should permit the western gate leading to Lod to remain open until the third hour, allowing whoever wanted to escape to do so and remain alive. Rabi Yohanan saved likely hundreds of thousands on that day. It was at least in a way a Chag Lashem.
Another answer may be found in the very last posuk of the Torah. It finishes with the words; “Moshe performed before the eyes of all Israel”: Rashi explains that this refers to the incident where Moshe Rabbenu smashed the luchos, as it is said, “and I shattered them before your eyes” (Deut. 9:17- Shabbos. 87a). These are the very last words of the Torah, the ones that we read on the great siyum on Simchas Torah and we eternally honor and rejoice with. Would it not have been more fitting to choose another more positive, appropriate and better chapter to finish the Torah with, than the pathetic making of the eigel, followed by the subsequent tragic braking of the Luchos? This likely was the worst day in the life of Moshe Rabbenu!
However, although the luchos were incredible precious and valuable to Moshe Rabenu who understood their true value and fasted forty days and nights for them. He was willing to brake them, to save the Jewish Nation. Hashem agreed with him and thanked Moshe for breaking the luchos. The sacrifice of Moshe Rabbenu to save the people is truly the Chag Lashem Mochor.
After the first churban the ninth of Tamuz became the fast day, since it did not reflect the above.

Rabbi A. Bartfeld