What's in a word?

I recently read a piece in a California newspaper about gay marriage.  The writer claimed that she felt many gay marriage opponents were falsely labeled as prejudiced because they objected to the use of the word marriage for same sex couples, not the act of commitment.  In her words:

I have no problem whatsoever with any people of the same sex who want to commit themselves to each other to do so. The issue is, find another word that explains the commitment of two people of the same sex. Marriage means something else — it's a different relationship.

I think every citizen deserves to receive all rights and benefits regardless of their choice of partner, simply find a word that fits your situation.

The question I would like to raise is why don't you want gay people to share that word with you? Why do you want sole ownership of that word?  I question whether or not it is reasonable to accept that there is no prejudice here.  There is enormous variety in the types of marriages in the world. Should second and third marriages have a different name from first marriages?  What about marriages with significant age differences between the spouses?  Should marriages that result in children be labeled differently from those that don't produce children?  What about interracial marriages from marriages of people from the same race?  I think most people would consider it demeaning to rename these marriages.  It is just as demeaning to insist that gay people need a separate word, as if our mere sharing of that word diminishes it.  And isn't that what any civil rights movement is about: insisting that the rights a privileged segment of the population claims to exclusively "own" be made available to other members of society?