In the time when the bible was written and was essentially law, if a woman was raped, she had to marry her rapist. Read deuteronimies if you don't believe me. Marriage seems to be heavily taken for granted as any asshole celebrity can have a heterosexual marriage for 42 hours to gain attention and then divorce immediately.
Rights are assumed and argued against; privileges are unassumed and argued for. These are no mere semantics.
For example: Freedom of speech is assumed to apply. Someone bringing an action for defamation is arguing against the applicability of that freedom. It is assumed that someone will produce all documents necessary to a court. A lawyer arguing for legal professional privilege for some documents is arguing for privilege.
For marriage, it is a pure legal right. It is not a privilege in any sense... it just happens to only apply to those in heterosexual relationships. They're 'privileged', but I'm using this word in a different context here.
A lot of what people call "rights" are actually privileges, but then, very often governments try to label privileges things that ought to be rights. That's why we have to be careful.
At base, marriage is a contract, and it's peculiar to say the least that this contract alone is strictly limited as to what sort of people may enter into it. If that was the case with any other contract, it would be immediately as wrong.