Well to Twilight Sparkle, Celestia is both her teacher and someone of royal importance, and when Celestia started giving her tasks such as reporting back about friendship and helping save the world, Twilight most likely didn't know how to normally approach all these new events. Her life suddenly became something like a big test, and she didn't want to fail her friends or her teacher, however she probably thought that her friends would accept her mistakes more than Celestia would. Heck she worried about Fluttershy being throwed in jail over Philomena, but did that actually happen? Nope it sure didn't, she overreacted to failure towards Celestia, even if it wasn't her own doing.
Everypony else, including Twilight's friends knows that Celestia is important, but they don't worry about her and what she does and such unless they have a real significant reason to. Twilight worries about what can happen and what Celestia could do, and makes it seem like if things doesn't turn out the way she believes it should be, then Celestia's reaction would be severe no matter what in the end. Twilight just didn't know how to handle it all, I'm sure none of her lessons or books would even come close to preparing her for what was in store for her, she had to rely on who she is and what she knew to get through it all. I wouldn't be surprised if Twilight studied and read about Celestia to try and figure her out like she does for questions she comes across that are difficult to answer on their own.
There's many variables to why Twilight would react to Celestia like she does, Twilight being the way she is, and Celestia being as important as she is (her role as a Princess), I guess the real question is would things have been the same if she didn't overreact like she does? Perhaps things wouldn't have turned out much differently, but it's just the way she is, no one makes her act that way on purpose, she just does it on her own.