Women give sex to get a relationship. Men give a relationship to get sex.
I don't agree with that saying at all. Just because you're fooling around with a gal, doesn't mean she's relationship-chasing you. It's not a rarity for a gal to be open to sex with a guy, without having a relationship with him on her vagenda. And women aren't "Giving" sex any more than the guy -- they're experiencing it just as much as the guy. They're not asexual beings, like utilizing sex as a tool to get a husband and to breed. We don't live in 1800s Mormon-land. :)
I think instead, the Common way things tend to go, outside of rebound-effect: Women have sex with a guy who, at the time, Feel is Dating-worthy... and guys have sex with a woman who's merely not Unattractive.