At the simplest level the PL is "incoherent" in the manner of an oxymoron. A little like saying it is possible to "communicate without communicating."
More to the point, it might be harder than you think to create your truly "private" language. In the first place, it would have be absolutely unique and, in theory, indecipherable. So you can't just "translate" the grammar and words of some language you already know by some term-grinding equation. Easily reverse engineered.
You might "randomize" or "scramble" an existing language by some operation. But if even you can find no "meanings" in the result, is it really your "language"? Finally, how would this language distinguish itself from the continuity of your "private" thoughts? It must somehow become discontinuous with your own thoughts while also modeling them... and then reappearing as "recognizable" to them. Hard to do entirely on your own.
And should you ever succeed, how would you convince others of your unique epistemological accomplishment?
I think Wittgenstein's point was, as usual, to draw attention to something rather obvious that gets lost only in philosophy, where so many projects begin in some sort of isolated inner dialogue. This is the epistemological version of what Marx called "Robinsonism," the propensity of modern thinkers to construct theories around some atomic Robison Crusoe who just appears there, spontaneously generated, with all his ideas and tools.