If we take evolution as our the model for our species then parents and parenthood are vitally important to the survival of the species.
At certain times peers might play a bigger role in forming who we are but to say that consistently peers are more important than parents, I think, is incorrect.
Some studies of the most closely related primates suggest that peers may be more important for them than parents are, as well as for humans.
How many people posting here are parents? I have four children. Since I have had my second child, I have cherished the saying I learned from another parent: "Parents of one child believe in nurture, and parents of two or more children believe in nature."
At certain times peers might play a bigger role in forming who we are but to say that consistently peers are more important than parents, I think, is incorrect.