“This phrase has completely lost its original, covenant-related, meaning…The original meaning is, "The blood of the covenant is thicker than the water of the womb," or, "My relationship with those to whom I am joined in covenant is to be considered of more value than the relationship with a brother with whom I may have shared the womb." You see, Jesus believed blood is thicker than water! Those with whom he entered into covenant were more important than even those with whom he shared his mother’s womb!
Jesus grew up in a typical Jewish family of his time, lots of brothers and sisters. Only one of his brother's became a believer, that Jesus was the Son of God. Thus began this fleshly brother's spiritual relationship with his half brother, Jesus Christ. This is the new covenant and did away with the old covenant.