Student: Can I borrow a pencil?
Teacher: I don’t know, can you borrow a pencil?
Student: Aha, but I clearly meant to ask for permission. Since you and the rest of the class understood my intent perfectly well, and the word “may” to show permission is rapidly falling out of fashion, there is nothing wrong with asking you whether I can borrow a pencil.
Teacher: Possibly so, in colloquial speech. Discerning context can help us decipher the nuance of each sentence on a case-by-case basis. However, as your teacher, my task is to teach you the intricacies and nuances of the English language with rigor, so that you may have a greater mastery of the language in order to effectively and precisely control what you want to communicate. In this case, the difference between the words “can” and “may”.
Student: Point taken. May I borrow a pencil?
Teacher: No, you may not. The state cut funding for education again.