Programmers often discover solutions while explaining a problem to someone else, even to people with no programming knowledge. Describing the code, and comparing to what it actually does, exposes inconsistencies. Explaining a subject also forces the programmer to look at it from new perspectives and can provide a deeper understanding.
I used to tutor college chemistry and calculus. I secretly sucked at both, but I knew what questions to ask students to start them thinking. They got excited to discover the answers while explaining it to me.