I'm not a native English speaker, however for me out of my league has a much broader range of application. That could be in many sports contexts, that could be intelligence or education etc. and of course appearance too. Basically anything, where you compare and rank and eventually compete.
Your English is really excellent, and you are quite right that the phrase can be used in different contexts. For example, I could say something like, "That guy is one helluva rounder, completely out of my league!" and it means that he is so much better than me at poker that I couldn't hope to compete with him. But in those usages too, "out of my league" does not *generally* mean the same thing as "not in my social class" as I understood
@Jbagz and some others to be claiming. My example makes it obvious (intentionally); ability to play poker is not a significant element of social class.
In dating appearance might be one major factor, but by far not the only one. Appearance is very likely the most common reason, why guys think a girl is out of their league, but surely not the only one.
I agree with everything you say in the quote immediately above, and I even agree that social class can be a reason someone might regard another as "out of their league" for dating purposes...happens fairly often in fact. But that doesn't mean "out of my league" always or mostly means "in a higher social class than me".
As far as I can see, the issue also doesn't have much to do with "social mobility" as I again understand
@Jbagz to be claiming. For example, if a sizzling hot 30-something guy who has done nothing with his life since high school except work as a waiter at a long series of downscale restaurants and spend his leisure time mostly drinking beer, partying and watching sports on TV manages to date a rather plain looking 30-something socialite from a wealthy family who has just completed law school and a celebratory 6-month long world tour before taking up a partner-track position with a big name NYC law firm, it does not mean either of them have changed their social class. All the other elements of social class are far more important than who they are dating.
The original question wasn't restricted to appearance afaik in so far social circles may be a viable answer as to why someone is supposedly out of reach.
The OP didn't even specify a dating dating context, to be sure, but given that it was on TAG and perhaps because
@Not Even Dave has recently been posting about dating women out of his league in terms of appearance (in other threads), I assumed (perhaps incorrectly) that we were primarily talking about appearance and dating here.
However, no matter the context, I don't think that "out of my league" is really all that close to meaning the same thing as "of a higher social class than me" even though ***some*** of the same factors affect both concepts; others are quite different.
Sorry to belabor this point at such length, but I think the discussion got pretty muddy and confused when it started conflating "league" with "social class".
-Ww