It's important not to jump to conclusions or read too much into a single invitation or event. People's motivations for inviting others to do things can be varied and not always indicative of romantic interest.
In this specific situation, it seems that the girl asked you to see the Barbie movie because she didn't have anyone else to go with, and she felt comfortable asking you. It's possible she sees you as a friend or simply someone she enjoys spending time with.
To understand her intentions better, consider the following:
Evaluate your existing relationship: Reflect on your interactions with her in the past. Have you been friends, acquaintances, or something more?
Observe her behavior: Pay attention to how she treats you and interacts with you in different settings. Look for any signs of romantic interest or simply friendly behavior.
Communicate openly: If you're uncertain about her intentions, the best way to find out is to communicate openly and honestly. You can have a casual conversation and ask how she sees your relationship and what her intentions were with the movie invitation.
Respect her feelings: Regardless of her intentions, it's essential to respect her feelings and be considerate of her perspective.
Remember, people can have different motivations for their actions, and it's crucial not to make assumptions without proper communication. If you're interested in her romantically, it's okay to express your feelings, but be prepared for the possibility that she may not feel the same way.
Ultimately, the best way to move forward is through open and respectful communication, which can lead to a clearer understanding of each other's intentions and feelings.