So much of our love is pedestrian. Express it for things, rather than people. And when it comes to people, we go halfway too often. The example of Jesus is contrary to that. When Jesus expresses his love, he goes deeper than we could have imagined. This is part of what the Aparecida bishops mean by love that surpasses human love:
543. An authentic evangelization of our peoples entails fully assuming the radicality of Christian love, which is embodied in following Christ on the Cross; in suffering for Christ for the sake of justice; and in forgiveness and love of enemies. This love surpasses human love and shares in divine love, the only cultural axis that can build a culture of life. In the Trinity-God, diversity of Persons does not generate violence and conflict, but is itself the source of love and life.
Pertinent advice for a violence-ridden planet:
An evangelization that places Redemption at the center, that is born out of a crucified love, is capable of purifying the structures of violent society and generating new ones. The radicality of violence is resolved only in the radicality of redeeming love. Evangelizing based on self-surrendering love as solution to conflict must be the “radical” cultural thrust of a new society. Only thus can the continent of hope reach the point of truly becoming the continent of love.
For deeper examination, check an English translation of the 2007 document from the Aparecida Conference.