If you want to know what the four dissenting Justices said, it boils down to this:
Roberts: The definition of marriage should be made by legislation.
Scalia: The Supreme Court has too much power any time it does not agree with me.
Thomas: Due process doesn't include the right to be married.
Alito: Power in this matter is reserved to the States individually. Also, the Supreme Court has too much power any time it does not agree with me.