As far as we can tell, Bar Qamtza comes off as something of a jerk. He is personally offended, so he actually joins with the enemy to take down his own people. A bit of a problem with anger and vengefulness. So it’s quite likely that the host actually had sound reason from previous interactions not to want him around, why the sages didn’t empathize with him.
The gemara gives us numerous reasons for why the Second Beis haMiqdash was destroyed.
|Important tangent: R’ Jack Love notes a pattern. There are numerous explanations of why Nadav and Avihu deserved death, what sin(s) lead to tzara’as, why the First Beis haMiqdash fell, the second, etc… He suggests that this in itself is the lesson. We grapple with why bad things happen, we look for meaning, but even Chazal don’t reach consensus, do not suggest they have the reason for the tragic.|
But of all the reasons the gemara gives, the one that captured the Jewish People’s attention was the idea that it was our sin’as chinam, our pointless hatred of each other, that led Hashem to end the Second Commonwealth. Perhaps because we realize that of the issues raised, it’s the one that we need the most work on.
But how does the gemara illustrate this point? Not by spelling out the animosity between this group and that group. But with the fact that we were able to give offense to a single, likely unsavory, individual and not even care. We held a debate over whether to offer an animal with a blemished lip or eye. How would the story have ended had the debate been over which sage would go to apologize?