Christianity has presuppositions. A major one - for Kierkegaard - is that people love themselves, since it is at the centre of Jesus' commandment to love one's neighbour. Here he provides some insights that are vague or missing in the previous chapter. For Kierkegaard - "self-love" is the love between friends and lovers, and is essentially self-motivated. It's easy to do, and people do it all the time - Jesus says the same thing. Loving your neighbour (i.e. anyone who is not you) as yourself is not self-love. He writes that Christians should be loving without distinction and favouritism, and therefore be free of self-love (which is based on favouritism).
Therefore "Self-love" must NOT be confused with "love your neighbour as yourself" - they are very different!
Despite what the "poets" may write it is neither good nor proper to love anyone more than oneself. This is something reserved only for God. Therefore, when we love someone as ourself we do not love them in a way that obeys all their wishes - unconditional obedience is left for God. The loving thing one does for others is what one would find to be the most loving for oneself. Anything more than this Kierkegaard deems as adoration - Kierkegaard doesn't use the word, but idolatry may be implied here as well. Love, in Kierkegaard's sense, is quite intolerant (given the modern definition of the word) and based on the moral grounding of the individual who loves, rather than the individual receiving love.
He writes that the command to love your neighbour as yourself is a complete and binding statement, something that doesn't require examples and theory, it's easy to understand and we know (if we love ourselves) exactly what our duty to our neighbour is. The only way out is to narrowly define who our neighbour is, but Kierkegaard insists that the neighbour can be no one else but the "other" - i.e. not you. People are neighbours whether they like it or not, the question is whether they fulfill their duty as neighbours.