Let us suppose, to see where this false assumption leads us, that premarital sex were morally permissible. Let us also suppose that marriage is a social institution and that a social institution is defined normatively by the duties and permissions one gains as a result of entering into the institution.
Now, all the substantive non-sexual duties and permissions of marriage can be had by a non-marital relationship (I say "substantive", because there is one permission that cannot be had except by those who are married, and that is the permission to say "we are married"). Two people who love each other as brother and sister (in fact, they could actually be brother and sister) could simply come together and through carefully written contracts (against the background of a state that gives sufficient authority to contracts) give each other the duties that marriage involves, and those permissions that depend on one another's agreement, and the state could then do the rest for them.
Thus, marriage, if it an institution, has to bestow sexual duties and/or permissions. Could this just be the duty not to have sex with anybody else? I don't think so. The two people who love each other as brother and sister could promise each other than neither would have sex with anybody, and then they would automatically acquire the duty not to have sex with anybody else (this is a controversial point—I know at least one philosopher who will deny the inference here). Since premarital sex was assumed to be permissible, the couple does not acquire the permission to have sex. So what sexual duty or permission do they acquire?
The only remaining plausible candidate is that each acquires a duty (surely a ceteris paribus one) to have sex with the other. Thus, if the argument works, then if (a) marriage is a social institution in the above sense and (b) premarital sex is permissible, then what defines marriage over and beyond a possible committed loving lifelong non-marital relationship is that by marrying the couple gives each other sexual duties towards each other.
This means that if we see marriage as a social institution, and we accept premarital sex as permissible, we will see marriage as basically a "stern" institution (here I am echoing Newman's idea of conscience as a "stern" voice, i.e., one that speaks only of duty), one defined by the conferral of duties rather than of permissions. On the other hand, if we see premarital sex as impermissible, we will see marriage as in large part a permissive institution, one that confers the permission to have sex.
Presumably seeing marriage as a stern institution is a part of why some people in our culture have a negative attitude towards it.