Do you mean “impossible in principle” or “will never be built by our civilization”?
If first, then it is a well-known an widely accepted without much evidence idea that brain just can’t be simulated by any sort of Turing machine. For in-story explanation why there are no AIs in future, that is enough.
If second, there is a very real possibility than technical progress will slow down to a halt, and we just never reach a technical capability to build an AI. On this topic, some people say that progress is accelerating right now and some say that it is slowing down since the late 19 century, and of course future is even more unclear.
That division is in fact not universal and not clear.
First, in some armies promotion of enlisted men and NCOs is or was in fact main source of officers. One example is German army before and during WWII. Link in Russian
In short, no higher education was required and training itself took 6 − 9 months.
Second, USA has warrant officers, USSR had (and some post-Soviet states now have) praporshchiks, and there are many more categories that are between enlisted and officers.
And reason why that two-ladder system with classist origins is not univesally abandoned as obsolete is simple: long education. To promote senior sergeant to leutenant you have first sent him to academy, and if that takes few years that is not really an option. So choice is between educated and experienced officers, and most armies choose educated.