I have to say, based on how she is shown in pictures and video clips she indeed comes across as arrogant. But I also remember Alexia as a small(er) child, where she came across as much shy and withdrawn. It seemed that Amalia was much more outward-looking (responding to the press, waving, laughing as a small child), while it often seemed too much to Alexia. It is possible that her parents acted on it and that it contributed to her arrogant appearance.
Very late to this discussion, but being very aware of how you look in photos (posing, wearing a lot of make-up etc) can be arrogance, but it can also often be indicative of things like insecurity about one's appearance, anxiety, nervousness and not feeling totally comfortable with having your photo taken. It sounds ironic, but some of my family tease me for being a "poser", but it is actually the opposite - I don't really like having my photo taken and I'm always trying to find a way to stand that doesn't feel so awkward. And unlike me, Alexia's family photos are going to end up all over the internet for the world to see. I worry about looking bad in photos that will only be displayed in my mother's living room and on her Facebook account where she has ~40 friends, so I can't imagine how Alexia and her sisters must feel, especially in those awkward teenage years. It is possible Alexia has tried really hard to beat shyness and her efforts to be more "out there" come off a bit badly.
Maybe she is arrogant. Maybe she is vain. Maybe she is an insufferable brat. Maybe we will see her being a spoiled socialite in a few years. But there is also the possibility that she is a perfectly nice teenage girl feeling kinda awkward knowing her family photos end up on the internet for the whole country to talk about and that awkwardness and desire to look "cool" (very normal for a 16 year old) comes across as arrogance. Either way, we don't know, and I 100% agree with this:
And she’s 16. Let’s let her grow up a bit before we condemn her.
I think she at least deserves the chance to make it through her teenage years and grow up a bit before being written off as a brat. I'm glad I wasn't throw into the public eye at 16 to be judged, because I personally matured a lot at University. Maybe she will go off to University and turn out totally fine and be a nice person. Maybe she will be an annoying Instagram model or another spoiled Euro socialite in 5 years time, but then at least we'd be criticising the actions of a 21 year old adult who has chosen to keep putting herself out there, not a 16 year old minor living out her awkward teenage years in the public eye when it was expected of her, not something she actually consented to.