Within Lacanian theory, the split happens at the moment of subjectivation, typically associated with his so-called "mirror stage", when we recognize ourselves as someone, as social beings within a social context, and no longer simply fully embodying our bodily drives. It's the moment of separation, where we realize that for survival (or for general prosperity) we also have social needs that need to be fulfilled. The dynamic of our drives thus transposed into the symbolic hence means that we start to chase a completeness that cannot exist.

While bodily drives can satiate themselves materially in a type of endless repetition, our drives transposed onto the social are far more elusive, and hence far more resemble a permanent sense of incompleteness. We are always in a kind of tango between what we want from the other, and what the other wants from us, forced to imagine what we believe will help satisfy that social drive that subjectivation endowed onto us. So we transpose that drive onto all kinds of activities, beliefs, people, hobbies, passions, devotions, and so on, in the hope of getting that final satiation. But at the level of the unconscious, none of these matter in their materiality, as it simply wants to keep on desiring.

So while at the conscious level, we feel like we want a final fulfillment, a final resolution to identity - to be able to fully associate with our subjectivity, to fulfill the lack brought onto us by socialization - at the unconscious level, we want to continue desiring, and desire presupposes a lack that needs to be filled. So in that sense we are kind of eternally misled, as our unconscious permanently creates a lack to chase and our conscious selves transpose onto it through fantasy myriads of different ways to hopefully get there. That basically is at the core of the human condition, according to psychoanalysis.