“It is to Joseph, then, that the messenger turns, entrusting to him the responsibilities of an earthly father with regard to Mary's Son.” – (Redimptoris Custos # 3).
Since St. Joseph was called to be the head of the Holy Family, does this in any way mean that his authority or that His decisions over his family were completely arbitrary? No. It had to be in accord with the will of God. “Then Joseph, arising from sleep, did just as the Angel of the Lord had instructed him, and he accepted her as his wife.” (Matt 1:24). Our Lord and Savior was subject to the human fatherly authority that God has given to St. Joseph, (which by the way, shows us the humility of Jesus by being obedient to His human parents (Luke 2:51), something that the prideful fallen angels could not accept in regards to human beings). Jesus "...was subjected to Joseph, he obeyed him and rendered to him that honor and reverence that children owe to their father" (RC # 8 ).
It is important to note that St. Joseph still worships Jesus notwithstanding his authoritative role over his family. St. Joseph could not have taught Jesus anything contrary to God’s teachings but, by God’s given authority and grace, he could also have disciplinary rules or decisions of the prudential order over his foster Son Jesus and also over his wife Mary. It is understood by Sacred Tradition that Jesus helped St. Joseph in the carpentry work. By the prevenient grace of God, these decisions or rules could not have been in any way contrary to the teachings of God either. “Joseph, who had the important task of "raising" Jesus, that is, feeding, clothing and educating him in the Law and in a trade, in keeping with the duties of a father.” – (RC #16). “And he [Jesus] descended with them [Joseph and Mary] and went to Nazareth. And he was subordinate to them…” (Luke 2:51).
John 3:27; John 15:5; Matthew 19:26