The phrase "The most attractive quality in a woman" suggests that the speaker considers this particular quality as highly appealing. What's being emphasized is not physical appearance but a certain mindset or set of values.
The quote values a sense of discernment and self-respect. When it mentions that a woman "hasn't been with everybody," it implies that she's selective in her choices of partners, which can signify a sense of self-worth and a desire for meaningful connections.
Likewise, the phrase "won't be with just anybody" suggests that the woman has standards and is not easily swayed by just anyone who comes her way. This can indicate a level of independence and a focus on forming connections based on deeper compatibility rather than settling for less.