I heard this perspective on Jesus as the perfect fulfillment of the Older Brother in a sermon somewhere recently, and I want to share it because I find it challenging and compelling. 

In ancient times the oldest son had a position of power and status over his siblings.  I can’t think of many good older brothers in the Bible; it seems that many of them were busy manipulating and exploiting their positions of power.  For instance, Esau foolishly sold his birthright and then tried to steal it back; Joseph’s older bros sold him into slavery; and Solomon's older bro Adonijah tried to seize the throne.  Older brothers had rights to more power and status than their siblings, and they tended to use this power for self-promotion.

Jesus entered this culture and served as the perfect Older Brother who used this status in order to lay down his life for the good of others.  Jesus was the firstborn (i.e. oldest) brother among all creation, including Christians.  As oldest brother, he had rights, priveleges, and status that we didn’t have.  But Jesus broke the Old Testatement type of older brother.  He didn't use his rights for self-promotion.  Instead, he sacrificed his power to suffer more than anyone else has ever suffered, all for the sake of his younger siblings – the Church.

By being the perfect Older Brother, Jesus taught us to sacrifice whatever power and status our culture gives us for the sake of serving others.  And he lived what he taught – if we want to be great, we need to lay down our lives.