One reason that I think friendship is so enjoyable is that it allows us to appreciate qualities in others that we do not ourselves possess. God has made each person unique – indeed, unrepeatable – and friendship gives us a chance to recognize the gifts of others. It can liberate us from some of the narrowness of our own point-of-view. While we possess certain qualities in common with our friends, I think that much of the pleasure we receive from friendship arises from the uniqueness we discover in others.
As a final comment, I would agree that ideal friendship is singular in nature. I think it describes the relationship we can share with God. We can have strong and vital friendships with others to the extent that we have this primary friendship with God, a relationship that, with His aid and our cooperation, will reach its fullness in the life to come. His love becomes the source and stimulus of our love not only for Him, but for others. Our friendships in this world can help prepare us for the self-giving love of beatitude, in which our union with God and our communion with others will finally be experienced as a single movement of love, as the gift of friendship fully realized and shared, corresponding completely to the desire and design of the human heart.