Jesus is the Son of God the Father. Inherent in the idea of submission is the concept of authority. The Bible, not to mention nature itself, teaches that fathers have authority over their sons. So also the Father has authority over His Son, and not the other way around. Thus within the Godhead equality does not mean equality of authority. A person's physical body may be considered one aspect of a person just as a person's soul and spirit are other aspects, and yet the body should be submissive to the soul and not act independently. For "trinity" is not "tri-theism".
"I tell you the truth, the Son can do nothing by himself; he can do only what he sees his Father doing, because whatever the Father does the Son also does." John 5:19The Father is greater in authority than Jesus
"the Father is greater than I." John 14:28But has delegated authority to His Son.
Then Jesus came to them and said, "All authority in heaven and on earth has been given to me." Mt 28:18So also believers have been delegated authority to make disciples of all nations as Christ's ambassadors. But even so in making judgements, Jesus still relies upon the Father.
"God placed all things under his feet and appointed him to be head over everything." Eph 1:22
"I have received authority from my Father" Rev 2:27
"Moreover, the Father judges no one, but has entrusted all judgment to the Son, that all may honor the Son just as they honor the Father." John 5:22,23
"By myself I can do nothing; I judge only as I hear, and my judgment is just, for I seek not to please myself but him who sent me." John 5:30So also when we make disciples, the message we preach and the manner in which we go about it should be in submission to the forms we find in the Bible.
Jesus being an independent person within the Godhead had his own will. But he submitted his will to that of his Father's.
"For I have come down from heaven not to do my will but to do the will of him who sent me." John 6:38So also we should not presume that whatever we feel like doing must be God's will for us. Rather we should question whether our will is God's will and submit ourselves in subservience to God.
"Father, if you are willing, take this cup from me; yet not my will, but yours be done." Luke 22:42