Finkelstein and Knowsnothing,
The term "criticism" does NOT mean to be critical or to criticise. As scholars use it, the term means to analyse, study, evaluate.
Let me give you an example: Higher Criticism could be seen as seeking to understand the cultural context of a particular piece. When was it written? By whom? What was their intent? What was their culture at that time?
You ask about Adam and Eve. This story was created about the 8th century BCE by the Yahwist priests/scribes at Jerusalem. We know this because they use the name YHWH before it was revealed to Moses. Their intention was to create a religious story that focused on marriage. Its structure and sequence of events contradicts the sequence of the Creation story (Gen 1:1 to 2:4a), which was written slightly later by a different group of priests/scribes. They used the name of EL for God until YHWH was revealed to Moses. The book "Who Wrote the Bible?" by Richard Elliott Friedman provides the details.
As you can see, this process treats the scriptures as literature, asking about the authors, intended audiences (they were not writing to us), subsequent editors, and so on. It also considers the various streams of documents, such as comparing and contrasting the LXX against the MT, the DSS, and so on.
The WTS is interested in the times of the neo-Babylonian Captivity. Much of the OT was created and recreated during this period (Deut, Isa 40-66, etc.) and aftwerwards.
Lower Criticism attempts to identify the correct text, getting as close to the original as possible.
I hope you see that this term "criticism" means to analyse and understand, not to criticise.
Why pick on Adam and Eve? Be more controversial and ask: Was there really a person named Moses? Was there really a massive exodus from Egypt?
Doug