Could they make the promises tacitly? That is without actually saying them? Many couples who live together without being married have tried this. The trouble with unstated, or unclearly articulated promises, is that the couple may not actually agree about what the real foundation of the relationship is. They may discover they have conflicting expectations.
Underlying these ideas is the presence of some kind of commitment to the relationship. Many kinds of relationships can have varying kinds of commitment as their foundation. Does the presence of a commitment constitute a marriage? In part that depends on the nature of the commitment.
What if two friends of the same gender decided to commit themselves to love each other, to the exclusion of all others, for the rest of their lives. Would this constitute a marriage? It fulfils one of the criteria – a commitment to love. But it doesn’t fulfil another criteria which both the Bible and human societies have generally assumed to be part of marriage: that the couple be one man and one woman.
Why does the couple need to be of mixed gender? The Bible would say that it has to do with the way God made humans. He made them male and female, and intended that they should become one flesh together in a union of male and female. That’s what is being united, or married: two different kinds of humans into one – to express and model a humanity that is male and female together.
Dale