Well, there are a few theories regarding as to why he wrote the Secret History, but the one that has the most credibility to me is that he became dissatisfied with Justinian's reign through a combination of Justinian's willingness to promote people to high station on merit alone and he tendency to heavily tax the nobility to finance his projects and simultaneously keep the from being powerful enough to oppose him. Procopius was rather stodgy and conservative fellow who was from old blood, and he didn't like the way Justinian did things AT ALL. As to why it wasn't destroyed, well 3 reasons really, the work was published posthumously, people have always loved smut, and for the longest time no one actually believed that Procopius wrote it, as such it didn't have the weight behind it that would necessitate imperial action. A lot of this in conjecture of course. Can we learn anything from it? Yes. We can use it to see what was culturally unacceptable to the nobility of the time, we can use it to conjecture what the burlesque lifestyle *might* have been like during the period, though its thought that Procopius is making most of the Secret History up.

For the actual historical part of this answer I referred to Judith Herrin and Warren Treadgold

Herrin, J. (2009). Byzantium: the surprising life of a medieval empire. Princeton University Press.

Treadgold, W. T. (1997). A history of the Byzantine state and society. Stanford University Press.