Why are superiors styled Father and Mother?

Superiors are styled Father and Mother, both to teach them in all duties toward their inferiors, like natural parents, to express love and tenderness to them, according to their several relations;[1] and to work inferiors to a greater willingness and cheerfulness in performing their duties to their superiors, as to their parents.[2]

1. Eph. 6:4

   Fathers, do not provoke your children to anger, but bring them up in the discipline and instruction of the Lord.

   II Cor. 12:14

   Here for the third time I am ready to come to you. And I will not be a burden, for I seek not what is yours but you. For children are not obligated to save up for their parents, but parents for their children.

   I Thess. 2:7-8, 11

   But we were gentle among you, like a nursing mother taking care of her own children. So, being affectionately desirous of you, we were ready to share with you not only the gospel of God but also our own selves, because you had become very dear to us.

   For you know how, like a father with his children

   Num. 11:11-12

   Moses said to the Lord, “Why have you dealt ill with your servant? And why have I not found favor in your sight, that you lay the burden of all this people on me? Did I conceive all this people? Did I give them birth, that you should say to me, ‘Carry them in your bosom, as a nurse carries a nursing child,’ to the land that you swore to give their fathers?

2. I Cor. 4:14-16

   I do not write these things to make you ashamed, but to admonish you as my beloved children. For though you have countless guides in Christ, you do not have many fathers. For I became your father in Christ Jesus through the gospel. I urge you, then, be imitators of me.

   II Kings 5:13

   But his servants came near and said to him, “My father, it is a great word the prophet has spoken to you; will you not do it? Has he actually said to you, ‘Wash, and be clean’?”

Question 125, Westminster Larger Catechism