May and Can. We might as well give up on this rule because the can-ites won the war. No one seems to have trouble with can, but my guess is that the use of may sounds too formal.
In school, most of us learned that may referred to authorization or permission while can denoted physical or mental ability.
“May I have this dance?” asks permission. But if you asked, “Can I have this dance?” you inquired about the potential partner’s physical ability.
Strict grammarians still insist on may as the polite way to ask for permission; however, for as long as most of us have been alive, either is now acceptable, except in formal situations.
This is a case where usage overturned rules.