This is a very interesting question. If you look at the animal world, almost all researchers would agree that although animals are a part of the world, they are not distinct selves. In other words, when a dog barks at its reflection in a mirror, it is not aware that it is barking at its own self. Only humans (and theoretically the highest level primates) may have this ability.
Human beings begin to understand self as a part of our social interactions. Several researchers conjectured that the self develops from the ability to see that you are separate and distinct from the environment and others. Erikson referenced this slightly in the stages of initiative versus guilt and autonomy versus shame and doubt, both of these stages requiring an understanding of self apart from others, but also requiring the interaction of society in order to maintain it.
Piaget would state that ones self develops from an understanding of object permanence where the concept that things exist even when not seen is established. This logical milestone paves the way for an understanding that "I" exist apart from other people and things. This is further enhanced when the concept of self is expanded through interactions with the world (society) and our individual psychology develops as a part of a basic building block of logic called a schema.
Existential-phenomenology would look at self as the development of "I" and "thou" through meaning that is achieved through social and environmental interaction. The idea here is that identity/self is established with the help of the environment and society, but the individual gives him/her self personal meaning through social reflection.
In feminist theory, the concept of self develops more from specific social interactions and modeling of healthy behavior than simply social interactions in a general fashion. Therefore, self is dependent upon society but only if that society is capable of giving an accurate reflection of self.
I hope this helps you,