Jesus, quoting Moses, says that the greatest good for a human is to love God with all our being and to love our neighbor as we love ourselves. This at least implies that self-love is good and healthy, but it places healthy self-love in the context of relationship.
We love ourselves truly when we find who we are in the context of our personal connection with God and others. Paul explains self-love the same way in Ephesians 5 – pointing out that for a husband to truly love himself he must give himself up for his wife like Jesus gave himself up for the church. In other words, good self-love happens when we love God and love our neighbor. The alternative is a self-love that values oneself over the other – a type of love which is destructive both of relationship and (counterintuitively perhaps) ourself as well.