As we go through life, we experience different stages, from childhood, through youth, adulthood and old age. There is to our internal sense an experience of continuity. We can reflect back through the preceding stages and recognize a consistent “person” that is experiencing these stages.
It is therefore quite natural for the first impression about rebirth to be based on the idea that this same “consistent person” moves from one life to another. Even among those who do not accept the idea of rebirth, but who believe in an eternal heaven or hell after death, the “person” experiencing these things is implied to be this “consistent person” we experience in a lifetime.
Sri Aurobindo describes it thus: “In the ordinary, the vulgar conception there is no birth of a soul at all, but only the birth of a new body into the world occupied by an old personality unchanged from that which once left some now discarded physical frame. It is John Robinson who has gone out of the form of flesh he once occupied; it is John Robinson who tomorrow or some centuries hence will re-incarnate in another form of flesh and resume the course of his terrestrial experiences with another name and in another environment.”
It is more or less akin to changing a suit of clothes for another in the most common iteration of this idea.
Sri Aurobindo points out that this idea is especially appealing. “For it is the extinction or dissolution of the personality, of this mental, nervous and physical composite which I call myself that is hard to bear for the man enamoured of life, and it is the promise of its survival and physical reappearance that is the great lure.”
The real problem, from the common viewpoint, is that we do not have any clear memory or sense of that continuity between birth and birth as we do within the framework of a single lifetime. We want to have the awareness of continuity and failing that we do not see the purpose or experience the positive enjoyment of the extended life of the “consistent person”. People who take this view therefore in some cases try to establish a continuity through practices such as “past life regression” therapy. Others provide explanations for the lack of memory, such as that propounded in the Aeneid, whereby when a man dies, he goes to the underworld, and when the time comes for returning to earth, he first goes into the river of Lethe which removes all memory of the past life.
Clearly there are limitations to the idea that a single “consistent person” moves from life to life, even if we acknowledge and accept the reality of the process of rebirth. It is simply more subtle and more complex than the common view of the matter.