Some in the past have understood covenant as a theological category that changes the way Scripture is views or sectioned. Covenant was an ancient term meaning a blood contract. There have been discussions in the scholorly realm about whether the covenant was undertaken by God alone or if man had any choice in the matter. Covenant theologians do not believe that man is capable of responding apart from Divine initiative. There are variations to how much and when God undertakes these intiatives in the "secret councils" of His Will and Purposes!
Others believe that there is an element in which man can or may respond. Wesleyans and the Methodist''s camps believe in previenient grace where God goes before, preparing the Way.
The Jews understood themselves as God's chosen people therefore, they segmented themselves off from others in their worship services. There was a way to become a part of the covenant and it was a ritual, in which, a man could be initiated into covenant. Other men and the women were left in the outer court (of course, the men and women were separated)...
I find this whole understanding of life very discombobulated. And the questions are many, but they are not new. I am beginning to find it ludacrous to believe, as religion does things in the name of God that is not understandable. Why would a rational person disregard another because of certain religious rituals? Why would they think he were a "dog"? I don't think religion breeds an environment where reason is liked or lived by...it is emotion, feeling, and experience.