MEI haven't read the work, but this is what I'm getting from the excerpt you've provided.
Kierkegaard is a Christian, so when he begins with, "A human being is a spirit," he is beginning with the a Biblical premise of man as a spiritual being in three parts - body, soul, and spirit.
Taken in the context of the entire excerpt, he equates these three parts with the physical man, the psychic man, and the self.
The two parts which are being "synthesized," in his view, are the physical man and the psychic man - or man's body and his mind, but not the part of his mind which deals with his identity, more so, simply, his cognitive functioning.
The self, the identity, is the byproduct, the negative - the third, of this physical-psychic interrelation.
>The self is a relation that relates itself to itself or is the relation’s relating itself to itself in the relation; the self is not the relation but is the relation’s relating itself to itself.
The self is the process of the psychic man relating to the body and vise-versa, and the experiences of the body - past, present, and potential.
It is not the relation itself, but the process of relating within the context of this physical-psychic relationship which births "self."
>In the relation between two, the relation is the third as a negative unity
In other words, it is a reflection of the interrelation between the body and the soul. I do not use the word "mind" because mind could potentially encompass the idea of self, whereas, for Kierkegaard, the soul is being equated with psychic functioning.
>Such a relation that relates itself to itself, a self, must either have established itself or have been established by another. If the relation that relates itself to itself has been established by another, then the relation is indeed the third, but this relation, the third, is yet again a relation and relates itself to that which established the entire relation.
This "self," or spirit, has either been birthed naturally out of the relationship between body and soul, or it was intentionally birthed by an outside force - for Kierkegaard, this is likely God. If it was created, he says, then it is truly the third part of this mind, body, spirit relationship, but even in that case it still is in the position of functioning as a byproduct of interrelation between the physical-psycho dynamics.
He concludes, therefore, that the spirit is a derivative of interrelationships which was created by an outside force, and because of that, must attempt to relate itself again, both to the context of the relationship between the psychic and the physical, and to the source of its origin - God, the infinite, or the eternal.