Extracted from "Can Only God Save?"
[Bracketed numbers are from original article]
Throughout the Old Testament, God says that He is the only Savior. Obviously this must be true because salvation is an infinite work, including as it must, the full payment of the infinite penalty for sin required by God’s infinite justice—something which only God could accomplish. Consequently, for Jesus to be our Savior, He must be God. Paul wrote, “God our Savior” (1 Tim. 1:1, 2:3; Titus 1:3 and 4; 2:10 and 13; 3:4) as did Peter (2 Peter 1:1) and Jude (v. 25)…Thus, God in His infinite love and grace became a man through the virgin birth so that He, as a man, could take the judgment we deserved and make it possible for us to be forgiven. 
The logic of this argument begins with the premise that only God can save. Beside the influence of pagan thought, this idea comes from the fact that God is called “Savior” in Scripture. For example:
Isaiah 43:11 I, even I, am the Lord, and apart from me there is no savior.
Because the above verse seems to say that God is the only savior, the argument is that Jesus has to be God in order to save us, and if he is not God, then he did not save us, and we will die in our sins. But this is a fallacious argument because it fails on several counts.
- First, it fails to recognize the distinction between God as the Author of salvation and Christ as the Agent.  God, Christ and others are all referred to as “savior,” but that clearly does not make them identical.
The term “savior” is used of many people in the Bible. This is hard to see in the English versions because, when it is used of men, the translators almost always translated it as “deliverer.”* For example:
Nehemiah 9:27 So you handed them over to their enemies, who oppressed them. But when they were oppressed they cried out to you. From heaven you heard them, and in your great compassion you gave them deliverers [“saviors”], who rescued them from the hand of their enemies.
This in and of itself shows that modern translators have a Trinitarian bias that was not in the original languages. The only reason to translate the same word as “Savior” when it applies to God or Christ, but as “deliverer” when it applies to men, is to make the term seem unique to God and Jesus when in fact it is not. This is a good example of how the actual meaning of Scripture can be obscured if the translators are not careful or if they are theologically biased.
God’s gracious provision of “saviors” is not recognized when the same word is translated “savior” for God and Christ but “deliverer” for others. Also lost is the testimony in Scripture that God works through people to bring His power to bear. Of course, the fact that there are other “saviors” does not take away from Jesus Christ, who is the only one who could and did save us from our sins and eternal death. 
- Second, the term “savior” must be understood in relationship to what people were being “saved” from. The “saving” that God did prior to His Son’s coming was rescuing His people from their various bondages and captivities, not the ultimate salvation of saving His people from their sins. That job had to wait until the birth of the man who was the Lamb of (from) God, not the God who became a Lamb.
- The third problem with this argument is that it fails to take into account a common idiom employed in prophetic utterances, namely that actions are often attributed directly to God when in fact they will be carried out by His agents. Matthew 1:21 (NRSV) says that the name “Jesus” or Yeshua means “Yahweh saves,” and proceeds to give a prophetic utterance based on the name: “for he will save his people from their sins.” His name means “Yahweh saves,” and yet it says that “he [Jesus] will save.” This kind of language has a rich biblical background that must be understood clearly to avoid confusion. [For further study read “Divine Agents: Speaking and Acting in God’s Stead.”]
Jesus, Yeshua, is the same name as the “Joshua” of Old Testament fame. By studying the relevant biblical records, we learn that Yahweh did not “save” Israel by doing the job Himself, or by becoming Joshua. Joshua “saved” Israel by obeying God and leading the children of Israel out of the wilderness and into the Promised Land. The salvation was wrought by God empowering both Joshua and the people who went forth in faith to claim the victory that God guaranteed for them if they would go get it. Yet leading up to this victorious accomplishment of Joshua’s were several prophetic utterances spoken by God Himself, strongly stating that He would do the job. For example:
Exodus 23:23,27, and 28 (23) My angel will go ahead of you and bring you into the land of the Amorites, Hittites, Perizzites, Canaanites, Hivites and Jebusites, and I will wipe them out.
(27) I will send my terror ahead of you and throw into confusion every nation you encounter. I will make all your enemies turn their backs and run
(28) I will send the hornet ahead of you to drive the Hivites, Canaanites and Hittites out of your way.
It seems very clear in verse 23 that God said that He Himself would do the delivering. But, in this same context a few verses later, He says that the Israelites will drive His enemies out:
Exodus 23:31 I will establish your borders from the Red Sea to the Sea of the Philistines, and from the desert to the River. I will hand over to you the people who live in the land and you will drive them out before you.
What is going on? Is God the “savior” here or not? The fact is, this is typical of prophetic language.  The principle we see over and over in Scripture is this: God says that “He will do” something that in fact He will empower His servants to do with His help. More specifically, when God says that He will do something, He means that He will send someone with whom He will work to bring His will to pass. In the above case, it was Joshua, but also Moses, Gideon, the other judges, David and many others were the active agents of the salvation that God “wrought.”  In the case of sending someone to die for our sins, He sent Jesus, the namesake of Joshua. Only rarely in Scripture does God act sovereignly (i.e., without a human agent), and in the case of Jesus, He did not take matters into His own hands, but entrusted His will into the loving and obedient hands of His beloved Son. God, as His manner has always been, sent the perfect person into the battle and worked with him until the job was done. So in a very real sense, both God and Jesus “saved” us, as Old Testament heroes saved Israel, and therefore it is appropriate that each should be called “savior.” 
We agree that Man, in his fallen condition, could never produce a qualified candidate for the job of Messiah, nor initiate anything resulting in the redemption of mankind. Because sin is inherent in mankind, and because the wages of sin is death, the death of a sacrifice was required to atone for it (Heb. 9:22). Animal blood, though provisionally adequate before Christ by the grace of God, failed to satisfactorily meet the requirements of a complete atonement. God, being spirit, has no blood; furthermore, God, who is immortal and eternal, cannot die. Therefore the only solution was that a man with perfect blood (that is, a sinless man) had to die. But because all men have been tainted by sin, there would be no possibility for a sinless human to exist without some kind of direct, divine intervention. However, we must reject the proposition that the only way God could satisfy the requirements of redemption was by becoming a man Himself.
Contrary to the assumption that Christ must be God for redemption to be accomplished, we find, upon closer scrutiny, that the opposite must be the case—that unless he was a man, Jesus could not have redeemed mankind. God’s “infinite” (we prefer a less mathematical and more biblical term like “immortal”) nature actually precluded Him from being our redeemer, because God cannot die. He therefore sent a man equipped for the task, one who could die for our sins and then be raised from the dead to vanquish death forever. This is the clear testimony of Scripture.
Romans 5:15 But the gift is not like the trespass. For if the many died by the trespass of the one MAN [Adam], how much more did God’s grace and the gift that came by the grace of the one MAN, Jesus Christ, overflow to the many!
If it were a major tenet of Christianity that redemption had to be accomplished by God Himself, then this section of Romans would have been the perfect place to say it. But just when Scripture could settle the argument once and for all, it says that redemption had to be accomplished by a man. The theological imaginings of “learned men” that only God could redeem mankind are rendered null and void by the clear voice of God Himself speaking through Scripture: a man had to do the job. Not just any man, but a sinless man, a man born of a virgin—THE MAN, Jesus, now The Man exalted to the position of “Lord” at God’s right hand.
The crux of the Christian faith is not a mythical and mystical “incarnation” by which God supposedly became a man, but the historical event of a purely righteous man’s death on a tree, and then his being raised from the dead by God to everlasting life. It is this simple but powerful truth that began to be exchanged for a “mystery.” 
According to Biblical Unitarians, what's wrong with this argument?
This is a primitive logic that disregards all other scripture that would inform a better and truthful understanding of the concept of salvation including how it is derived and through whom is it delivered.