Tisha B'av is the saddest day on our calendar. It is a day of mourning and tears, not introspection. Usually, when we fast, we do so to sharpen our focus and enable us to concentrate on repentance and improvement. For a day, we completely put aside our earthly needs and focus instead on our spiritual imperatives. On Tisha B'av we don't eat because we can't, because the idea of taking food on such a desolate day is more than we can bear.
"The Sages taught in a baraita (Tosefta, Sota 15:11): When the Temple was destroyed a second time, there was an increase in the number of ascetics among the Jews, whose practice was to not eat meat and to not drink wine. Rabbi Yehoshua joined them to discuss their practice. He said to them: My children, for what reason do you not eat meat and do you not drink wine? They said to him: Shall we eat meat, from which offerings are sacrificed upon the altar, and now the altar has ceased to exist? Shall we drink wine, which is poured as a libation upon the altar, and now the altar has ceased to exist?" -- Babylonian Talmud, Baba Batra 60b.
It is natural to react to tragedy with withdrawal, self-denial and even abnegation. And we do. For one day. For the rest:
"Rabbi Yehoshua said to them: My children, come, and I will tell you how we should act. To not mourn at all is impossible, as the decree was already issued and the Temple has been destroyed. But to mourn excessively as you are doing is also impossible, as the Sages do not issue a decree upon the public unless a majority of the public is able to abide by it." -- Babylonian Talmud, Baba Batra 60b
However, on that one day, we take our leave to vent the full range of emotions. They can be grief, despair, and even anger at G-d. The kinnot (liturgical mourning poems) we recite are rich in these images, even occasionally sarcastically asking Hashem how he could treat us so. That process is a crucial part of mourning. It is an essential part of dealing with tragedy. It is, above all else, an illustration of our relationship with Hashem. When the day is over, we allow our emotions to die down to a simmer, and the intensity of our grief reduces. We allow our relationship with the divine and with our people to comfort us, going into Shabbat Nachamu. That is the message and the power of Tisha B'av.