What is the etymology of the word marriage?
Marriage, and the related word "matrimony" derives from the Old French word matremoine, which appears around 1300 CE and ultimately derives from Latin mātrimōnium, which combines two concepts: mater meaning "mother" and the suffix -monium signifying "action, state, or condition".
In ancient Rome, a man who entered into this state with a woman was, by that act, promising to confer upon her the title of "mater" or mother, especially a mother who bears children who can inherit. Children who can inherit property are said to have "legitimate" rights to property, in contrast to "bastards", who are defined as children without even theoretical rights to inherit property. If a legitimate heir died, the family property would go to a cousin or other near relative, but could not be given to a bastard child, if only because the man had not conferred legal status to inherit upon the mother he conceived with or her children conceived by her.
The state of matrimony was a legal state that concerned children's rights of inheritance. Love had no necessary standing in that legal relationship. While many other meanings have been added to the word "matrimony" over the millennia, this basic meaning is still retained, and is still foundational.
So, to put it simply, matrimony/marriage is the gift of legitimate children bestowed by a man upon a woman. By impregnating her within a legally binding agreement, the man confers upon the woman the title "mother" and confers upon their children the right to property.
Once this is understood, it is easy to see why "same-sex marriage" is a nonsense phrase.