Exegesis of Galatians 3:20 ( Now a mediator is not for one party only; whereas God is only one )
Galatians 3:15-22 New American Standard Bible (NASB)
15 Brethren, I speak [x]in terms of human relations: even though it is only a man’s [y]covenant, yet when it has been ratified, no one sets it aside or adds [z]conditions to it. 16 Now the promises were spoken to Abraham and to his seed. He does not say, “And to seeds,” as referring to many, but rather to one, “And to your seed,” that is, Christ. 17 What I am saying is this: the Law, which came four hundred and thirty years later, does not invalidate a covenant previously ratified by God, so as to nullify the promise. 18 For if the inheritance is [aa]based on law, it is no longer [ab]based on a promise; but God has granted it to Abraham by means of a promise.
19 Why the Law then? It was added [ac]because of transgressions, having been ordained through angels by the [ad]agency of a mediator, until the seed would come to whom the promise had been made. 20 Now a mediator is not [ae]for one party only; whereas God is only one. 21 Is the Law then contrary to the promises of God? May it never be! For if a law had been given which was able to impart life, then righteousness [af]would indeed have been [ag]based on law. 22 But the Scripture has shut up [ah]everyone under sin, so that the promise by faith in Jesus Christ might be given to those who believe.
Old Testament Law
God (1st party)---Moses (Mediator)---Ancient Israelites (2nd party)
( Now a mediator is not for one party only...) In the aforementioned quasi-diagram, I can understand the meaning of the biblical scripture "Now a mediator is not for one party only..." because it suggests that Moses the Mediator is supportive of both parties( God & the Ancient Israelites ) or for lack of a better term or phrase, one could say Moses the Mediator is unbiased as the middleman between God and the Ancient Israelites.
New Testament Promise
God (1st party and the person Jesus Christ as Mediator )---Church(2nd party)
( whereas God is only one ) Is the aforementioned scripture verse saying that Jesus Christ is Mediator only for God? Is it like saying he is Only supportive of God? Is it biased towards God?
Reference: The New Testament commentary for schools, ed. by C.J. Ellicott edited by Charles John Ellicott (bp. of Gloucester) (20) The mention of the word “mediator” implies a contract to which there are at least two parties. But where there is a contract there must be also conditions, and if these conditions are not observed the whole falls to the ground. Such was the Law. The Law was not kept, and therefore the blessings annexed to it were forfeited. On the other hand, the promise depends upon God alone. He gave it, and He will assuredly keep it, no matter what man may do. God alone is concerned in it.
This passage is a conspicuous instance of the advance which has been made in New Testament exegesis. It is said to have received as many as 250 or 300 (according to another estimate, even 430) interpretations, but at the present moment there is a tendency to acquiesce in that given above, which, it is hoped, will be thought satisfactory.
Now a mediator is not a mediator of one.—The very idea of a mediator involves two parties at least. The Law had a mediator, therefore the Law involves two parties. In other words, it is a contract.
But God is one.—On the other hand, God, the giver of the promise, stands alone:
therefore the promise is not a contract; and, resting on God, it is indefeasible.
@anne raises a very good counter argument:
The sign of that covenant was circumcision, which was a big problem in Galatians 2 vs 12. Jewish Christians had to grasp that it was circumcision of the heart that counted as the sign of the new covenant in Christ - Gal. 5:5-6. This point contradicts the quote you give that says “the promise stands alone: therefore the promise is not a contract”. Genesis 12:1-7, followed by the sign of circumcision, shows that Abraham agreed to enter into a covenant contract, even though God had shown He would personally pay the price of covenant obligation failure.