aquovary
Annaliese wants to go beyond the walls, not to prove a point, or slay all the titans and free humanity. That would be nice to achieve, but highly unprobable for her to do on her own. She wants to go beyond the walls because she believes that there's a world out there free from titans. It's a stretch, but something she believes in.
When Wall Maria fell, Annaliese was visiting her best friend, Jean Kirstein, in Trost. Her mother never showed up to retrieve her, and no one knew where her father was. Maybe he survived outside the walls on an expedition, but he had no idea where to find Annaliese.
So, the Scouts became the only way for her to obtain her possibly careless dream, and for her to find out if her father was alive. With Jean by her side, she felt like she could make it.
She knew she had to keep her mind and heart in check, and keep her morales straight. It wouldn't be too difficult of a task, would it?
She didn't realize how wrong she was.