Brave

It is interesting how Brave begins by depicting the restrictions and limitations of being a Princess. Highlighting the discrepancies between what Merida's brothers can do and how she "can't get away with anything" as she is held to a different standard. "A Princess rises early, is compassionate, cautious, patient, clean" her mother teaches Merida and the viewers. When Merida genuinely enjoys herself, she is berated for "chortling" and behaving in a manor not accustom to a Princess.
One of the most poignant pieces of 'advice' Merida's mother gives her is:
"and above all, a Princess strives for...well, perfection"
This is because it fits so well with Duke's studies of the cycle of effortless perfection and the pressure this puts on women to achieve it all without looking like they're breaking a sweat. This dramatically highlights the double standards held for males and females. The little Prince's are able to run wild and do not receive strict training, like Merida, nor are they expected to strive for or even attain perfection. Yet, Merida is set on a grueling task to chase unattainable perfection. Now this hardly seems fair! And this is what Pixar/Disney highlight through Merida's narrative. They're showing that 'Princess' isn't always what it's glamorized to be; in reality it can be restrictive and unfair. Brave is showing that we should encourage and nurture girls to follow their own passions, not what may be 'expected' of them because of their gender.

Merida explains that she enjoyed most her days where she didn't have to be a Princess because there were "no lessons and no expectations". In reality, Merida doesn't magically stop being a Princess on this day, she still has the same birth-right, she just has freedom to do what she wants. So this shows that Merida equates Princess with limitations, and sees her freedom of choice as not fitting into the role of a Princess - hence, her days off from this role. She sees this as "A day I can change my fate" and by the end of the film she has achieved this - she has changed society's perception of "Princess" and the notion of marriage too. Now, the next generation are able to take control of their own lives, choose their own future partners, and enjoy their own pursuits in life.

Even as a young child as Merida's father gives her a bow for her birthday, which she is evidently delighted at, the mother is upset that this isn't a gift for a lady.

Merida becomes a very skilled archer, shown to the viewers as she gallops through the forest hitting each target with precision. Merida excels in that which she enjoys, archery, and she struggles with that which is forced upon her, Princess lessons. An important message that can be gleamed from this is that we shouldn't force children into things, or stifle their passions. Success, to an extent, follows happiness.

Brave focuses on the relationship between Merida and her mother.
At the very beginning of the film, Merida and her mother are shown to be close. Playing in the field together on her birthday, and laughing and cuddling, they share precious bonding moments. However, this relationship definitively changes as Merida grows up, and is expected more and more to act like a lady. Her mother is preparing her for her future as the lady of a household - as a Queen. The forced instructions put a divide between the two, and lead to feelings of resentment on Merida's part and frustrtation on that of her mother's.
At the dinner table, Merida's mother doesn't listen to her adventures and shows no interest in what Merida's passions. This is followed by Merida being informed of her future betrothals, and consequently rebelling to try to regain control of her own life: "no it's what you've been preparing me for your whole life, I won't go through with this, you can't make me". This feisty, new-age Princess is not afraid to stand her ground against her parents in a matter as important to her as this.
The real relationship breakdown is shown as Merida acts out and slices the family tapestry following this incident, and her mother burns her bow (though does rescue it shortly after, clearly regretting the fight they've had).

Now, throw in some Disney style magic, and next thing you know, the mother is transformed into a bear. This is a very obvious struggle that the two must overcome together, repairing their relationship in the process. I particularly love the speech Merida gives to the room full of men, as her mother-bear signs across the room to her. Through this speech, we see the mother's change in attitude and acceptance of Merida, and this helps bring happiness and harmony to a place of previous discord.