The meaning is most likely from this definition of fast:
a : wild
b : sexually promiscuous
From Wiktionary:
Having an extravagant lifestyle or immoral habits [from 18th c.]
And from Etymonline:
The sense of "living an unrestrained life" (usually of women) is from 1746 (fast living is from 1745).
Without delving too far into literary criticism, the preacher's daughter, Sabbath Lily, is often the victim of men in the novel and is later revealed to be a nymphomaniac. So this sense of the word is undoubtedly what was implied.
I am struggling to make sense of the poetic insight the author has perceived in the situation depicted, and embedded in this phrase. I start by accepting that she has made an observation that she wants to communicate, so I take it that there is in fact a meaning here. I think this is important, because there really does not have to be any specific meaning beyond some evocative impressionistic observation that can't be communicated in words. It's also important for me to point out my process, because I want to emphasize that, at best, all I'm doing is making an educated guess as to the meaning, and only the author could have explained it precisely. The rest of us can only surmise.
And I think it means one of two things.
The first possibility is that "nerve" means simply "courage," and the necessity comes from either the fact that courage demands of a person that he or she act in a particular way, or the fact that these people feel the need to show their courage for others to see.
The second possibility is that "nerve" means what it does in the phrase "you've got some nerve." This use of nerve equates to "arrogant gall" or "impudence." If this is the meaning, I would then say that this kind of "nerve" carries its own necessity of expressing itself. If you're impudent, you act that way by your very nature.
The larger context of this quote, which would give us a better idea of the circumstances and the character of the people involved, would likely help us interpret it even better, but this is the best I can do with what we've got.
Best Answer
It means the same thing as "I like girls." The connotation is slightly different and the reason for including "just fine" is to counter the accusation that Nathan does not like girls.
An example in a different area:
The expression is used as a basic or stoic acceptance or acknowledgement. Other words with similar usage is "okay" or "alright". Each carry their own typical uses and connotations but the gist is there. A wordier way to say it:
Notes: I was interrupted while answering so there are more than the typical amount of edits. I apologize for any confusion.