Why are there so many instances of younger female characters falling in love with older male adult characters? Is it a cultural thing?
It is something that occurs everywhere and in all media. Just look at Lolita, which was published in 1955 and features a relationship as you describe it.
I think need to be a bit clearer in your definition of "younger female" and "older male" though. A 16 year old girl falling in love with a 18 year old boy would fit your criteria too.
I take it you mean something more along the line of CardCaptor Sakura's Yoshiyuki Terada and Rika Sasaki, where she is a primary school student and he her teacher?
Things like this actually happen in real life too. Though most people in that kind of situation wouldn't want their relationship to be know for legal and social reasons.
The difference between Japanese and American (as an example) media coverage of topics like this is that in Japan, as long as no real child is harmed it's a-okay (at least as far as I know), and if there were problems they could just as well say it's a 800 year old god just looking like a child. But in America a lot of people see it as catering to pedophiles and forbid it. Just look at all the interesting discussions about the freshly licensed and heavily censored "Monster Monpiece".
So even if it is an innocent relationship with no intimate contact it would be highly frowned upon in the US, while in Japan they'd just shrug their shoulders because no harm was done to anyone.
More generally speaking though: some people just like a more mature partner. Just look at Hugh Hefner and his girls (let's just all innocently assume they're not all after his money).