The story in Gittin about Kamtza and Bar Kamtza is one of three stories of how three different cities were destroyed. Kamtza and bar Kamtza is how Yerushalayim was destroyed. The Gemara about Sinas Chinam being the cause of the second Beis Hamikdash being destroyed is in Yoma.
Chazal had an understanding of what the Beis Hamikdash stood for and what each Beis Hamikdash separately stood for. They knew the depth of each Mitzva and their effects. The Gemara in Shabbos lists different Aveiros and their punishments. Some are from Pesukim, others are from their broad understanding that they gleaned from the Torah.
With their keen judgement, they were able to see what shortcoming was prevalent and if it co-relates to the Churban.
If you want an insight into what I’m talking about, see the Maharal’s Netzach Yisroel.