The fast of the 9th of Av begins on Saturday, August 9th. The terrible events that happened to the Jewish people on that date are well known, so our sages decreed a day of fasting similar to Yom Kippur (with the exception that on Tisha B'Av it is permitted to do melachot, that is, it is not like a Shabbat and one can travel, carry, etc.).
However, along with the decree to treat the day in a most solemn and serious manner, our sages decreed that Tachanun should not be said during prayer.
Tachanun are supplications that are recited every day except on holidays. They learned this from the fact that the Torah refers to the ninth of Av as Moed, which is the word used to refer to festivals (such as Passover, Shavuot, etc.), indicating a connection between these different holidays, making the ninth of Av "a festival"...
Now then: If the 9th of Av is a holiday, then let's celebrate as on other occasions, with wine, meat, etc., but if the 9th of Av is not a holiday, then why don't we say supplications for forgiveness in the prayer?
The Talmud (end of the tractate Makkot) contains a story that will help us understand this. The story goes like this:
Once upon a time, Rabban Gamliel, Rabbi Elazar ben Azaria, Rabbi Joshua, and Rabbi Akiva were traveling to Jerusalem. When they arrived at Mount Zofim, they tore their clothes. When they reached the Temple Mount and saw a wolf emerging from the Holy of Holies, they began to weep, and Rabbi Akiva laughed.
They said to him, "Why are you laughing?" He answered, "Why are you crying?" They replied, "The place where it is written, 'And the stranger who approaches will die,' now wolves walk in it, and shall we not weep?""
[Rabbi Akiva] said to them: "That is why I laugh, because it is written 'And I appoint as my faithful witnesses Uriah the Kohen and Zechariah son of Yebo-e-chahu,' what is the relationship between Uriah and Zechariah? Uriah lived during the First Temple and Zechariah during the Second Temple! [The relationship is that] the Torah made the prophecy of Zechariah dependent on the prophecy of Uriah. Uriah said, 'Therefore, for your sakes, the Blight [will be] plowed like a field, etc.,' while Zechariah said, 'The old men and old women will sit in the streets of Jerusalem.'".
Until Uriah's prophecy was fulfilled, I feared that Zechariah's prophecy would not be fulfilled; now that I see that Uriah's prophecy has been fulfilled, I know that Zechariah's will be fulfilled.
They said to him: "Akiva, you comforted us, Akiva, you comforted us.".
What is the difference between Rabbi Akiva's vision and that of his companions? Rabbi Akiva's companions saw the reality we live in. There are wolves in the holiest place of the destroyed Temple. We are in Exile, meaning the Divine Presence is hidden. Rabbi Akiva saw the beginning of the Final Redemption within the destruction itself.
However, this does not mean that Rabbi Akiva was naive and ignorant of the situation he was living in, which is why the story itself tells that "When they arrived at Har Tzofim, they tore their clothes," an action that even Rabbi Akiva carried out, expressing the appropriate level of mourning for the destruction of Jerusalem and the Temple.
In other words, a Jew must live in the current reality, but never be carried away by the current thinking that this is reality, but rather what our flesh and blood eyes see is only the outermost layer of a multifaceted reality.
That is why on Tisha B'Av, we fast, we do not sit in normal chairs, we modify the usual prayer and other laws and customs that lead us to live the reality of the worst day of the Hebrew calendar, but, nevertheless, we do not say supplications in the prayer, to express that the true reality of that day is one of redemption for all the Jewish people, which will be revealed to our flesh and blood eyes quickly in our days.