Self-identies, encouragement and failure

I learned that students' opinions of their own math abilities differed from others' opinions of their math abilities. I found this so interesting and helpful to know because it reminds me that students need constant encouragement in the classroom to develop and grow in learning mathematics. 
I was also reminded that students have the right to fail. Teachers deprive them of valuable learning opportunities by not allowing them to fail.
I still wonder how to strike the right balance between letting students fail enough to learn, but not so much that they become discouraged.