"[K] talks about a subjective thinker but not about subjective thinking. Kp's always talk about subjective thinkers not subjective thinking where K describes subjective thinking as anything other than abstract and universal."
Please consider these quotations from CUP (Hong, translation all quotes from Chapter II "Possible and Actual Theses by Lessing")
"Whereas objective thinking is indifferent to the thinking subject and his existence, the subjective thinker as existing is essentially interested in his own thinking, is existing in it. Therefore, his thinking has another kind of reflection, specifically that of inwardness, of possession, whereby it belongs to the subject and no one else. Whereas objective thinking invests everything in the result and assists all humanity to cheat by copying and reeling off the results and answers, subjective thinking invests everything in the process of becoming and omits the result, partly because this belongs to him, since he possesses the way, partly because he as existing is continually in the process of becoming, as is every human being who has not permitted himself to be tricked into becoming objective, into inhumanly becoming speculative thought." (pp. 72-3)
"The difference between subjective thinking and objective thinking must also be manifest in the form of communication. This means that the subjective thinker must promptly become aware that the form of communication must artistically possess just as much reflection as he himself, existing in his thinking, possesses." (pp. 73-4)
""Ordinary communication, objective thinking, has no secrets; only doubly reflected subjective thinking has secrets; that is, all its essential content is essentially a secret, because it cannot be communicated directly." (p. 79)
"One who is existing is continually in the process of becoming; the actually existing subjective thinker, thinking, continually reproduces this in his existence and invests all his thinking in becoming." (p. 86)
The expression "subjective thinking" occurs three times in the above quotes always in a wholly positive light.
I agree that Climacus uses the expression "subjective thinker" (or "subjective existing thinker" or "existing subjective thinker" see page 91 for example) more often than he uses the phase "subjective thinking. However, I ask you what does the subjective thinker essentially do? (Clue think of the individual's description as a "subjective THINKER")
The subjective thinker "exists in his thinking" (p. 74), he "invests all his thinking in becoming" (p. 86)
For the subjective thinker, to exist just is to think subjectively, to be in the process of becoming is to be thinking subjectively.
My conclusion: Objective thinking is non-essential and can legitimately be applied only to non-ethical and non-religious matters; subjective thinking is essential to the subjective thinker, and is wholly good, and whole worthwhile. One can never do too much subjective thinking. To think subjectively is to exist.