Problems With The Term "Woke" And A Potentially False Mathematical Implication

Possibly the biggest problem I have with the woke movement is the choice of the term it uses to represent itself.  It's not called "social justice woke" or "sexual orientation woke."  It's simply called "woke."  While this might simply be born out of convenience because one word is a much quicker and easier abbreviation for a concept than three words, I still think this possibly inadvertent simplification seems to imply a level of awareness that stretches far beyond its reach.  

While social injustice awareness is certainly not a bad thing, I believe it becomes a bad thing when you imply that's the ONLY skill anyone is required to possess in this world in order to be classified as fully aware and enlightened to the point that no other knowledge or skills are required.  Even if you can't count or read, and you've never expended any effort beyond sitting around and doing drugs all day, you're still fully aware of everything that matters simply because you recognize bigotry exists?  I would disagree, because I would argue that bigotry recognition is a NECESSARY but INSUFFICENT condition for cultural awareness and enlightenment.

The words necessary and sufficient form an important pair of terms in mathematics.  When a two related conditions in a statement fit both of these criteria, the statement carries a special kind of relationship between conditions known as a biconditional.  Biconditionality implies equivalence.  True in both directions.  Necessary implies truth in one direction and sufficient implies truth in the other direction.  What I claim regarding bigotry awareness and true enlightenment is that the two conditions are NOT connected by a biconditional.  Instead I claim these two things:

1) If one is fully enlightened, then indeed one automatically possesses an awareness of social justice problems

2) However, if one possesses an awareness of social justice problems, that person is still NOT automatically fully enlightened, because true enlightenment and awareness has other unrelated requirements as well

Notice with these two conditions, the flow is automatic in one direction but not the other.  It is a conditional statement but not a biconditional statement.  For two conditions to be equal, the biconditional must be satisfied, so that if either one of the conditions is satisfied, the other will automatically be satisfied as well.  That's not happening here.  So the two conditions are not equal.  Being truly enlightened is not equal to being aware of social justice issues.  Why?  Because being truly enlightened requires more than just that alone.  When one condition or set is strictly bigger than another, like true enlightenment encompassing more than just social justice awareness, they can't be completely equal.  Even if social justice awareness is the BIGGEST part of being truly enlightened, it's still not fitting all the requirements for full enlightenment and awareness.  

Now it might seem petty on my part to make a claim that the woke term implies far more than it does, and honestly it might be some kind of a stretch.  I believe the formal phrase for that type of petty stretch action now is seeking a microaggression.  Is that something that's permitted in two political directions or only one?