Chapter 3 has three basic points as there is a shift in the book to a more positive description from a reactive teaching model. 
I think the first point is the weakest and least helpful. The chapter opens with a description of the changes in social understanding of inter-racial marriage. This is interesting and I have just finished reading about the same thing in the book Committed. Committed, I think actually makes the argument of the changes better. When the Supreme Court decided Loving vs Virgina, overturning the Virginia ruling and allowed inter-racial marriage, 70% of the US disagreed with the ruling. But just a generation later, you will be hard pressed to find anyone that would say that inter-racial marriage should be prevented by law.
But the argument by really does not make a difference because friendship is not marriage and race is not gender. Yes, social conventions change. But the church, nor sin, is bound by societal convention.
The next two discussions are what I think are the heart of the rest of the book. Within the church, non-related people are biblically referred to as ‘brother and sister’. This reference is meant to describe a new relationship that comes about because we all are children of God the Father. Brennan then takes is language and uses it to understand a new way to describe cross-gender friendship. We all agree that biologically (and this is also true for adopted) brothers and sisters can have an intimate, physically affectionate relationship that is still platonic and non-sexual. In fact, most of us would be disgusted or at least offended if it were suggested that we had an inappropriate relationship with our sibling.
This model of understanding, Christian brothers and sisters, I find very useful in describing how we can have an intimate, yet chaste, relationship. This still does not mean that we must have intimate relationship, but rather than we may have intimate relationships. Sisters and brothers do not have a close relationship be because they are physically related (the closeness still must be worked on), but we do not find it odd when there is a close relationship.
The final illustration is from history, primarily the close relationships of medieval monks and nuns or priests (as confessors) and women laity. I find this illustration less helpful because there are many examples of people doing all kinds of things that we might now find inappropriate in history. But it is useful to say that cross gender friendships are not necessarily sinful
So what do you think, are any of these descriptive models useful for you?
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Other chapter discussions: Ch 1, 2, 3, 4, 5, 6, 7
I did find the anecdotes and stories about cross-gender friendships in church history to be moving and refreshing, particularly that of Frances de Sales and Lady Jane (sorry, my book is lent out and I forget her surname). The language used between them is powerful, the passion amazing. I suppose I’m not being exactly objective; just speaking from my own perspective.