Marriage, according to Genesis 2.
Genesis 2:24 Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh.
Genesis indicates that the man (and woman) remain with his/her father and mother until they are married. Only when married are they considered to be independent of the parents and become one flesh. The cycle then continues.
This would give the authority of the parents to arrange marriages, give away the daughter to a future son-in-law, etc.
The idea that man and woman should be sleeping around (experimenting, etc.) until marriage doesn't seem to be Biblical, as fornication is a sin. Virginity, then, should be kept by both the man and woman.
The problem, as I see it, is that God's design has been replaced with selfishness and pride—the root of sin.