Your daughter is now old enough to be self conscious about herself as a learner. As a toddler and as a preschooler, she just explored everything she could find. I wonder what other people think about my accomplishments. Now, at 10, she is old enough to imagine how others might be perceiving her. She is also at the age where she is setting challenging goals for herself.
All children experience self-consciousness, peer pressure, and impatience with their own learning.
But there are also some children who, because of their temperament, are more likely to be frustrated with their learning process or hesitant to try something new until they feel they are close to mastery. You probably know best whether your daughter's feelings result mostly from temperament or from developmental issues. Listen to your daughter's concerns. Often there are underlying concerns when a child breaks down and starts criticizing herself. Acknowledge what she has already figured out.