This is an appeal from the decision in A Local Authority v JB  EWCA Civ 735. In the part of the hearing to which you refer, Lord Stephens is asking the appellant’s counsel about the following principle, quoted at  of the judgment under appeal:
When considering capacity to marry, the question is whether X has capacity to marry, not whether she has capacity to marry Y rather than Z. The question of capacity to marry has never been considered by reference to a person's ability to understand or evaluate the characteristics of some particular spouse or intended spouse: Re E (and Alleged Patient); Sheffield City Council v E and S  EWHC 2808 (Fam).
In Re E, Munby J said at :
The point is suggested by Miss Waddicor's very pertinent rhetorical question: Can it seriously be suggested that the court has the right to vet E's suitors, to decide that X is suitable but that Y is unsuitable, to select who E is to marry? The answer to that question, in my judgment, is that the court quite clearly has no such role.
The ‘father of the bride test’ is the proposition rejected here: that the Court of Protection could play the traditional role of the father of the bride, by granting permission to marry a particular person, rather than determining the person’s capacity to marry in a more general sense.