An Olympic-inspired insight into the right to marry:
In mixed doubles tennis, each team consists of one man and one woman. By definition, neither two men nor two women may play together in this sport.
Now that's about as far as the analogy goes, but since a tennis match is largely free of the heavier baggage of human relationships, one aspect of the equal rights argument becomes clear.
Everyone has the right to play on a mixed doubles team, but no one has the right to a partner of the same sex. The basic right to play applies to the individual player, not the team.
It is likewise with marriage: An individual person has the right to marry, by definition, a person of the opposite sex. The right to marry belongs to the individual, not to the couple.
This is not to be confused with the fact that certain rights or privileges may accrue to a married couple (since for society, marriage is found to be very good). But the more fundamental right to even enter into a marriage pertains at the level of the individual.