Given my inability to elaborate upon 2 Corinthians 10 "on the spot," I have included a sample of a technical commentary on the passage. It is more than most of you will want to know, but nevertheless I thought you might benefit from it and perhaps enjoy a taste of a resource dealing with the Greek text.
"Paul’s second example of his “demolition of strongholds” is his overthrow of “every proud obstacle that sets itself up against the knowledge of God.” In an abstract sense ὕψωμα means “height” (Rom. 8:39) or “exaltation” (Job 24:24; Jdt. 10:8). Applied to physical military defenses, it refers to “what is lofty,” a “fortress with high towers” (G. Bertram, TDNT 8.614), or a “rampart” (Moffatt). Related to such usage is the metaphorical sense of “arrogant attitude” (Thrall 597), “towering conceit” (Isaacs), “presumptuous notion” (NJB), “proud obstacle” (RSV, NRSV). Reinforcing the notion of literal or figurative “elevation” that is intrinsic to ὕψωμα is the present participle ἐπαιρόμενον (from ἐπαίρω, “raise up”), which is not middle but passive, whether it means “ (that is) raised up”/“erected” or “that rises up/raises itself up.” This ὕψωμα is no neutral “lofty thing”; it is set up or sets itself up “against” or “in defiance of” (κατά) the authentic knowledge of God. Standing between λογισμούς and γνώσεως, the expression πᾶν ὕψωμα is likely to refer to every type (πᾶν) of idea or argument that is capable of preventing people from arriving at true and emancipating knowledge, the knowledge of God (τοῦ θεοῦ, objective genitive) through the gospel of Christ. There is a contrast between certain λογισμοί which must be overthrown and ἡ γνῶσις τοῦ θεοῦ which must be promoted, between impersonal argumentation and personal knowledge, and between false and true knowledge. Paul’s campaign strategy was not to ignore, dismiss, or ridicule his opponents’ ideas and arguments, but to “demolish” (καθαιρέω) them by exposing their fallacies. For him such demolition was indistinguishable from God’s “thwarting” of “the cleverness of the clever” (1 Cor. 1:19, citing Isa. 29:14). In speaking of his καθαίρεσις of λογισμοί and πᾶν ὕψωμα, Paul is certainly not denigrating rational thought and logical argumentation. His own letters are replete with careful and convincing argument. It is not “reasoning” as such that is attacked here but fallacious reasoning and conceited argument" (Murray J. Harris, 2 Corinthians).