I suppose it depends on what "out of their league" is.
Family Background, Education, Wealth, or Attractiveness.
Anytime one feels inferior to another they will have challenges, insecurities/jealousy and self doubt lurking beneath the surface.
A part of them can't believe this "great" person could be seriously interested in them. They are always waiting to wake up from the dream. One of the reasons for this is most of them believe if they were this "ideal person" they would not date someone like themselves. Some people compare themselves to their mate's exes. If he/she was better looking or earned more money it bothers them as well.
The only way to get over this type of thinking is to focus on one's own strengths.
Anybody who has someone it is because they bring something to the table. No one spends time with anyone who has absolutely NOTHING going for them. Instead of worrying about what might happen we'd all be better off living in "the NOW" It's been said, "Yesterday is a canceled check, Tomorrow is a promisory note, Today is CASH in hand."
Since both sexes are capable of being jealous or insecure depending on the circumstances I would say it all comes down to the individual and not their sex.