Mesites is built on mesos, middle. A mesites is the man who stands in the space between two parties. In the Greek world he was an arbitrator, a guarantor, sometimes an escrow agent: the trusted third party who makes a transaction between two others possible.

Scripture uses the word carefully and sparingly, and every use is worth counting. There is one God and one mesites between God and men, the man Messiah Yeshua, 1 Timothy 2:5. Hebrews calls Him the mesites of a better covenant, and then of a new covenant, and then of a new covenant again. Five uses in the Brit Chadashah, and every one of them is either about Yeshua or about Moshe at Sinai. Not one of them describes a continuing human office.

That matters more than it looks. Protestants have said the middleman is retired for five hundred years and they are right about mediation. But notice what the mesites in Hebrews actually mediates: the covenant of Yirmeyahu 31, quoted in full two verses later, in which no man teaches his neighbor any longer and all know Him from the least to the greatest. The one mediator Scripture permits mediates the arrangement that dismisses everyone else standing in the middle. If a structure keeps a man permanently positioned between you and the knowing of God, it is not doing what a mesites does. It is doing the thing the mesites came to end.