Why was nanon afraid of men's hands?

She says that men have always pawed her. But she's obviously a fairly young woman, maybe only 16 or 17, so the suggestion is perhaps that she was pawed even as a child. It is therefore at least possible that her father -- who seems to be the owner of the carnival -- molested her as a child. Alternately, perhaps a number of the members of the troupe had molested her, both as a child and after she developed. Often when such things happen the perpetrator makes the child promise not to tell; she may never have told her father. Or perhaps her father knew or suspected that some of the carnival people were improperly touching his daughter, and that is why he didn't like to see any man, even Chaney, with her.

It's implied to be the result of men constantly "pawing" and leering at her. She might have even been molested.