This Halacha is an excerpt from our Sefer
The 9th of Tammuz:
Although the verse states that the walls of Jerusalem of the 1st Temple were breached on the 9th of Tammuz, nevertheless we only fast on the 17th of Tammuz.
The reason for this is because: The breach of the walls on the 9th of Tammuz were by the times of the 1st Temple, while the breaching of the walls of the 17th of Tammuz were of the 2nd Temple, and the destruction of the 2nd Temple is of more severity towards us, [it was thus instituted to fast on the 17th as opposed to the 9th] as to fast both days is too much of a trouble for the public [and thus since the 17th is more severe, we therefore fast on the 17th.]
The custom of a Baal Nefesh: Nevertheless a meticulous person should also fast on the 9th.
The claim of the Jerusalem Talmud: Nevertheless in the Jerusalem Talmud it is brought that the breach of both walls occurred on the 17th, and the verse which had written that it occurred on the 9th had made a mistaken calculation. [Thus accordingly to this there is no reason for even a meticulous person to fast on the 9th]