The first wedding involved Adam and Even and God. Institutional involvement is not necessary. However, pre-marital sex is potentially destructive. If someone decides to move on after a physical relationship, whatever diseases, children, and emotional carnage left behind might not matter to them.
Chastity until marriage is a way to insure that as two people discover the physical aspect of their relationship, often with patience and even humor, they build a special intimacy that can last a lifetime.