Ordinary knowledge has a structure: someone knows something by some means. Vedanta calls this the triputi, the triad of knower, knowing and known, and observes that every act of cognition without exception has this shape. You know the tree because you are positioned as the subject and the tree is positioned as the object. The structure is so basic that it is invisible, and it is the reason Brahman cannot be known in the way anything else is known.
The argument is short. Brahman is the awareness in which all knowing occurs, which places it permanently on the subject side of the triad. For it to be known in the ordinary sense it would have to appear as an object, and whatever appears as an object is by definition not the one it appears to. An eye can see everything except itself; a scale can weigh anything except its own weight. The limitation is structural rather than a shortcoming that better instruments would fix.
What Vedanta proposes instead is not a superior method of objectification but the removal of a mistake. The texts are precise that Brahman is not attained, produced, reached or arrived at, since all four verbs imply distance from something already present. What ends is the misidentification analysed under adhyasa, and what is left over is described as self-evident: aparokshanubhuti, direct and unmediated, needing nothing to reveal it because it is what does the revealing.
The unknowability of Brahman is not mystical vagueness. It is a consequence of what knowing is. To see the specific error that has to be removed, explore more of The Living Sanatan Timeline.
Part 11 of 100 — Series I: From the Beginning
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