What right is being denied? Marriage is a union between a husband and a wife, a man and a woman.
That's actually just empirically false.
Same sex marriage is performed or at least recognised if performed elsewhere in South Africa, Argentina, Spain, Portugal, Canada, Belgium, Norway, Sweden, the Netherlands, Iceland, Israel, Brazil (recognises marriages performed in Alagoas) and Mexico (recognises marriages performed in DF).
In the United States, Connecticut, Iowa, DC, Massachusetts, New York, New Hampshire, Maryland, and (currently) California do not define marriage the way you do.
All up, that's over
600 million who live in areas where the definition of a recognised marriage is not restricted to "husband and wife". Including roughly 130 million in the United States (ie, about 40% of America).
And the trend-line is only running in one direction. It won't take much for, in the United States, "solely between a man and a woman" to be the
minority definition of marriage. If New Jersey, Washington and Oregon change, this would become the case.