Patricia and Wesley Galloway could not have children of their own. Yet for them, the essence of marriage is rooted in procreation. “It takes a man and a woman to create children and thus create a family,” Mrs. Galloway, 60, told a legislative panel in Connecticut last year as it was considering a bill to legalize same-sex marriage. The bill never went to a vote, but on Friday the Connecticut Supreme Court eliminated the need for a bill when it struck down the state’s civil union law and ruled that same-sex couples have a constitutional right to marry. The decision...