It’s not necessarily the same as how other people read the Bible. Denny Burk of Southern Baptist Theological Seminary breaks down the President’s scriptural justification for same-sex marriage:
… neither Matthew nor Jesus intended the Golden Rule to be a permission slip for debauchery. “Doing unto others as you would have them do unto you” does not nullify the Bible’s clear teaching about marriage and sexuality. The Sermon on the Mount affirms and intensifies Old Testament sexual norms (e.g., Matthew 5:27-30). Moreover, Jesus himself affirms the creation principle that defines marriage as the union of one man and one woman (Matt. 19:4-5; cf. Gen. 2:24). To imply that Jesus would have supported gay marriage has no basis in the text of scripture. In fact, Jesus stands against it.