What does out of league mean?

Answer 1

"You're out of my league" - means that you're too good for me (Also, means that "I don't deserve you")

"I am out of your league" - means that you're not good enough for me (Also, means "I deserve someone better")

Hope this is clear for you.

The term is a metaphor for sports leagues, which are often divided into a league for beginners or non-athletes playing for fun, then step-by-step upwards to the A league, which is for the best amateurs in town. On top are the professional / Olympic hopefuls.

Likewise, many people expect the prettiest women to date the handsomest men & rich people to date rich people. So if a working-class, average-to-ugly boy asks a rich, gorgeous girl for a date, "She's out of his/ your league," means he is unrealistic if he expects to date her because she can have any guy she wants, so why would she want him?