The Plot: In Disney's 2010 reinvention of the classic fairy tale, young Princess Rapunzel is kidnapped by the nefarious Mother Gothel.
Gothel raises Rapunzel as her own, keeping her locked up in a tall, secluded tower. Obviously, this means that Rapunzel has limited entertainment, so she'll often just gaze out the window. While doing this, she begins to notice a huge collection of lanterns being released into the sky, on the same day every year - her birthday.
These lanterns prompt her to leave the tower and investigate their source - against Gothel's wishes - an action which pushes the movie's story into motion.
How It Could've Been Resolved Quickly: Turns out those lanterns are released by Rapunzel's people, a way for the kingdom to remember their lost princess on her birthday, and a signal to her should she still be out there somewhere.
So why would Gothel tell Rapunzel that "lantern day" is also her birthday? She kidnapped her as a baby, so could have given her any birthday she chose. Why not give Rapunzel a birthday that's months away from the launch of the lanterns?
This way, Rapunzel would be less likely to assume that the lanterns were somehow linked to her, reducing her desire to leave the tower, and making it easier for Gothel to keep her around.