Question Restatement :
What was Eve's role in relation to Adam?
Note: I added another related question, to examine the word "before", Genesis 2:18 - How to interpret “before”, in “helper before him”?. That other question can falsify or validate this answer.
This interpretation is dependent on how one chooses to understand "Before", either as:
- "Helper who goes before as a champion / advocate"; or
- "Helper who submits before".
Because of the context and the ways "נגד | neged" is used in Hebrew, I think "champion" is merited : either to hold Adam accountable, or to champion for him, probably both.
HEB: אִישׁ֙ עֹמֵ֣ד לְנֶגְדּ֔וֹ וְחַרְבּ֥וֹ שְׁלוּפָ֖ה
NASB, Joshua 5:13-14 - Now it came about when Joshua was by Jericho, that ... a man was standing opposite him with his sword drawn in his hand, and Joshua ... said to him, “Are you for us or for our adversaries?” 14 He said, “No; rather I indeed come now as captain of the host of the Lord.”
Given the context - that Adam was to die that very day - Eve's role seems to stand out: 1.) She previously challenged the reasoning of the Serpent, on Adam's behalf; 2.) And, she provided Adam a valid defense, by pointing to their own vulnerability, and the Serpent that had deceived them.
Either way, Adam's life appears to have been spared - because of what Eve had done.
This interpretation also makes sense, in a the Systematic Theology view : that all of Scripture is about how advocating for others, unconditionally, in love, supersedes any judgments under law.
Challenging someone is a necessary part of advocacy; and, advocacy doesn't mean approval.
There are very few, if any, narratives in Scripture that don't convey this theme.
Conclusion: I think valid arguments could be made that Eve was to be a submissive helper for Adam, but "valid" doesn't mean right. At some point, it comes down to "Reader's Choice" - and in this case, I feel that a "noble interpretation" of Eve as an Advocate and Champion - is the correct interpretation.