"A person in despair wants despairingly to be himself…. The self which, in his despair, he wants to be is the self he is not (indeed, to want to be the self he truly is, is the very opposite of despair)…. To be ‘self’ in the way he wants to be it, that would be — even if in another sense just as despairing — everything he desired; but to be forced to be ‘self’ in a way that he doesn’t want to be, that is his torment — not being able to be rid of himself."
Soren Kierkegaard explains The Sickness unto Death. Binx Bolling’s “search” is just a way to rid himself of the despair he feels in his everyday life — the despair that comes from the gap between the life he lives (despite how happy he claims to be) and the life he and his aunt etc. feel he should be living.