In the article 'THE WORD MEDIATOR USED DIFFERENTLY' Zion's Watch Tower, January 1, 1909, pp.11-12 states :
Your attention is called to our use of the word Mediator in the seventh line of the article, "Homing the Ark," page 308, October 15th issue. We there speak of the "officiating priest who acted as the mediator between God and the nation." It would have been better had we used a different word on this occasion; for instance, advocate. Strictly speaking the Law Covenant constituted the bond of union between God and natural Israel, and Moses was the mediator of that covenant. The priest, strictly speaking, was not the mediator, but, under the terms of the Law Covenant, which Moses mediated, the officiating priest was the advocate, friend and representative of the Israelites before the bar of divine justice.
This well illustrates the too careless manner in which we, and nearly all Christians, have been accustomed to use this word mediator. For instance, repeatedly in DAWN-STUDIES, Vol. V., we refer to our Lord as the "Mediator of the Atonement." This is entirely correct, if judged by the ordinary standards of our language as generally used by us all. Of late, however, this Journal has endeavored to draw the attention of the Lord's people to the fact that the Bible uses the word mediator in a restricted sense and has urged that all Bible Students endeavor to take the Bible viewpoint only and to use the word mediator from that standpoint alone.
The correction above made shows how difficult it is for any of us to rid himself of the habit. The use of the word mediator in the Scriptures is restricted to the mediating of covenants between God and man.