Why You Should Affirm Dyothelitism and not Monothelitism

Dyothelitism is the idea that "will" is not a property of personhood but of nature. This might sound small, however it is actually very important, as affirming one doctrine will lead to a bunch of other doctrines. Thus, in dyothelitism the one person of Christ has two wills (Human and divine), although the human will is in perfect obedience to the divine will, thus there can be no conflict.

Dyothelitism is the historical view which has been taught by most Christians, including Evangelicals, Lutherans, Reformed churches, Roman Catholics, Orthodox and others. However, in more recent times some Evangelicals have proposed monothelitism, most known of which is William Lane Craig. 

Lewis Sperry Chafer affirmed
 dyothelitism

Among the dispensationalist Free Grace theologians, the historic doctrine is dyothelitism, not monothelitism, as we see from these quotes:

A similar error developed after Chalcedon that taught that Christ had only one will though conceding verbally that He had two natures. It is called monothelitism. This was condemned at the third council of Constantinople in 680. A study of errors should help clarify the truth and make us more careful how we express it. Semantics are very important in the statements of theology. (Ryrie, Basic Theology)

 The Scriptures declare that Christ possessed a human body, soul, and spirit, and that He experienced those emotions which belong to human existence. Much difficulty arises when the thought is entertained of two volitions—one divine and one human—in the one Person. Though this problem is difficult, it is clearly taught in the New Testament that Christ, on the human side, possessed a will which was wholly surrendered to the will of His Father. The surrender of the will, while it obviates any possible conflict between the will of the Father and the will of the Son, does not at all serve to remove the human will from His unique Person. The human will was ever present regardless of the use He may have made of it. (Lewis Sperry Chafer, Systematic Theology) 

 Biblical basis

Dyothelitism follows from the biblical fact that Christ was fully human, He must have had a human will for him to be in "every way like us":

Hebrews 2:17

Therefore in all things it behooved Him to be made like unto His brethren, that He might be a merciful and faithful High Priest in things pertaining to God, to make reconciliation for the sins of the people.

Hebrews 4:15

For we do not have a High Priest who cannot be touched with the feelings of our infirmities, but was in all points tempted as we are, yet without sin.

We also see in verses such as Philippians 2:8 that Christ "became" obedient, showing that when Christ became human, His human will fully obeyed the Father, as we see in in John 6:38. 

And being found in the fashion of a man, He humbled Himself and became obedient unto death—even the death of the cross.

The word "became" implies that it did not happen before the incarnation, thus when Jesus says "For I have come down from heaven not to do my will but to do the will of him who sent me.", it must be referencing the human will of Christ, not the divine will.

Although there is a specific order in the trinity (the Father sends the Son, the Father and the Son send the Holy Spirit), the bible says that Christ submitting His will to the Father is something that happened only after the incarnation.