You know, it’s really kind of a sad comic in both directions, when you think about it. I mean, putting aside the intentional bluntness Flurry Heart is using to hurt her mother, being a part of a royal family and a special one in a million individual (natural born alicorn and all) would probably be stifling for a teenager.
You have all the usual rebellious tendencies of others your age, but your actions and indiscretions are under constant public scrutiny and threat of being the next bit of late night comedy material. It would be a fairly high pressure lifestyle to have to lead, and she may have every bit of legitimacy in wanting to be normal for a bit.
That said, it’s a tough thing for the parent as well, because for them pushing too hard, even in kindness, has a chance of backfiring like it did here. Best they can do sometimes is to make it clear they care, that they’ll be there if they need you, and hope you’ll actually remember that when it matter most.

That said though, this is heartrendingly sad. You can imagine Cadance working day and night to clear her schedule enough so that she can have some time with one of the most important ponies in her life, only to be insulted and kicked to the curb for her efforts.

-Background Pony #7BC3