Authority given to man
What Jesus is saying is a reminder and reiteration of the first words spoken to Adam. “Procreate, fill the earth, subdue it and rule over it.” The triune God had transferred his authority to Adam and his descendants. Scripture goes on to be specific in Genesis that Adam would have the authority over every living creature, even to name them and also his wife. Eve was not created with different dust of the earth. She was taken from Adam. Both are equal but with entirely different gifts and responsibilities.
John writes in Chapter 1 that in the beginning, Christ (Logos) was the creator of all things. Therefore, when Jesus spoke to the disciples and now to us, he was reminding them one last time of his complete authority, even from day one. This was his last message before he ascended back to the throne where he is continuing to manage his creation through us. We are his vice-regents.
Authority within your family
Dads, you have a specific, God-ordained authority within your family. It is to execute what Christ has commanded. Make disciples. In your home and beyond, wherever the Lord directs. You cannot fail, his transferred authority will ensure success. Not perfection, but the pursuit is what he requires of us. There are many elements of discipleship, all outlined in Scripture. Seek the counsel from the word through the guidance of the Holy Spirit. He will teach you all things necessary for your success. What a joy to be trusted with his authority. Use it, don’t lose it!