AB,
The logical impossibility is the ability to apply logic without the need for conscious control.
That's not an argument for a logical impossibility at all – it's just an unqualified assertion with no reasoning of any sort to justify it. In any case though, even if we agree that it's as close as you're likely to get to an argument, that argument isn't sound (in this case because it's just an argument by assertion).
No matter how many times you stamp your foot and repeat the same idiocy of "to make argument I must be controlling my thoughts" that's still false (or no) reasoning so the claim fails on its face. In short: the argument should precede the conclusion, not the other way around.
Try to grasp this, and then to remember it the next time you're tempted to make the same mistake.