Marriage is an institution between a man and a woman.
Wrong. That's objectively incorrect in virtually the entire free world.
Almost all of the developed democracies in the world define marriage as the union of a couple, regardless of race, sex, or sexual orientation.
There is barely a civilized country left that uses your definition.
You really might want reconsider the morality of your backward beliefs: all the way back in 2004, when religious bigots attempted put your definition into the Constitution of the United States, Coretta Scott King (one of the leaders of the African-American civil rights movement and the wife of Martin Luther King Jr) publicly denounced those attempts as a form of "gay bashing". The proposed amendment failed, as even back in 2004 it was considered to be discriminatory, hateful, and repugnant.