True, the fasts, including Tisha B'Av, will ultimately become days of celebration.
Zechariah 8:18 And the word of the LORD of hosts came unto me, saying: 19 'Thus saith the LORD of hosts: The fast of the fourth month, and the fast of the fifth, and the fast of the seventh, and the fast of the tenth, shall be to the house of Judah joy and gladness, and cheerful seasons; therefore love ye truth and peace.
My rabbi said the Mashiach is expected to be born on Tisha B'Av.
Yes, it is known that Moshaich is born on Tish B'Av...
http://www.askmoses.com/en/article/110,43879/Is-it-true-that-the-Messiah-will-be-born-or-was-born-on-Tishah-bAv.htmlIs it true that the Messiah will be born (or was born) on Tishah b'Av?by Rabbi Naftali Silberberg
The Midrash1 relates that on the same day the Holy Temple was destroyed, Moshiach was born. The Midrash goes so far to tell us his name: Menachem.
Traditionally this is understood to mean that indeed Moshiach was born on that day, and had the Jews of that generation merited redemption, Menachem would have been revealed as Moshiach and immediately redeemed the Jews from exile.2
On a deeper level the Midrash is relating that the concepts of Moshiach and Redemption were "born" on Tishah b'Av; as soon as the Holy Temple was destroyed, redemption became a possibility. For if the Jews would have properly repented immediately, Moshiach would have been revealed at that moment.
In the teachings of Chassidut it is explained that the inner purpose of the destruction was so that we should be able to reach much higher spiritual levels with the coming of Moshiach - and this only became possible on Tishah b'Av.
So while today we view Tishah b'Av as a sad and tragic day, in the Messianic Era we will celebrate this day as the "birthday" of the ultimate salvation.3
Footnotes
1. Midrash Eicha Rabba 1:51
2. In every generation there is a person who can be Moshiach if that generation so merits. (See R. Ovadiah of Bartenura, Commentary on Ruth). For more about the personality of Moshiach see
http://www.chabad.org/library/article_cdo/aid/101679/jewish/The-Personality-of-Mashiach.htm3. Sources: See for example Likutei Sichos vol. 29 pp. 9-17