"We shouldn't care" does not necessarily follow from "nothing lasts". The loss of various impermanent things have caused me (and most people) a great deal of sadness.

A jackass with far more money and power than respect for it or anything else is tearing down a place where I have had a great number of memorable, fun, or significant interactions. There are important people in my life who very likely would not be if not for Twitter, including my spouse. Through Twitter I have helped connect people in ways that made significant changes to their lives. So yes, I'm sad, I'm frustrated, I'm annoyed, I'm angry, and I don't think it's irrational to feel those ways. I'm also annoyed at people acting superior because they're lucky enough to not be affected.