Self, person, living being, and life span are four notions that prevent us from seeing reality.
Life is one. We do not need to slice it into pieces and call this or that piece a "self." What we call a self is made only of non-self elements. When we look at a flower, for example, we may think that it is different from "non-flower" things. But when we look more deeply, we see that everything in the cosmos is in that flower. Without all of the non-flower elements - sunshine, clouds, earth, minerals, heat, rivers, and consciousness - a flower cannot be. That is why the Buddha teaches that the self does not exist. We have to discard all distinctions between self and non-self.