An excerpt From Torah.org:
The Rambam writes that the wise and the prophets should desire the arrival of Moshiach not because the stature of the Jews will have changed for the better, nor because they can then rejoice, but rather because they will be free to study the Torah without distraction.
Exile is a time when we are all burdened with worries and afflicted by persecutions. Exile is not conducive to Torah study. With the start of the siege of Jerusalem, our exile effectively began. The splendor of the Torah began to dim. For the first time in our history, we were not in the optimal setting for Torah study. We were in a decline.
With the death of Ezra years later, the distance from the proper method of Torah study increased. With the translation of the Torah into Greek, we fell to a new low: not only were we in exile, but we were faced with the new challenge a translation presented.
The three events that the Fast of the Tenth of Teves commemorate (siege of Jerusalem, death of Ezra, translation of Torah) share an unfortunate common denominator: a decline in diligent Torah study. This decline started with the siege of Jerusalem and remains with us until this very day.
It is very clear what pain we are still suffering from that stems from the events of the Tenth of Teves. We should all feel this pain. We should all realize what a great loss we have been afflicted with.
Most importantly, we should implement the words of the Rambam by reminding ourselves of these matters, so that we repent and improve our conduct.