Hoare partitioning scheme in Quicksort
&quot;The devil is in the details&quot;. Algorithms and programming, fortunately and unfortunately, needs the greatest attention to detail.
The part of code that are critical here are the following three groups of the code interleaved with comments. The first two lines of code is how to do the recursion. The middle one line of code is how to choose the pivot. The last two lines of code is how to determine the index that will be used by that first two lines of code to split the part of array between lo and hi.
#
# code skipped here
#
        quick_sort_hoare(A, lo, p)
        quick_sort_hoare(A, p + 1, hi)
#
# code skipped here
#
    pivot = A[lo]
#
# code skipped here
#    
        if i &gt;= j:
            return j  

The above version, as in OP's post and as in Wikipedia, is correct.
However, as mentioned by OP, the above version with its middle line of code changed to pivot = A[hi] will run into an infinite loop if given an array of more than one element whose unique largest element is its last element. A simple example of such an array is $[0,1]$ or $[1,0,2]$.
When the Wikipedia page says &quot;there are many variants of this algorithm, for example, selecting pivot from A[hi] instead of A[lo]&quot;, it means the following variant. On first look, nobody would expect this change of pivot would require code at two other places be changed. However, it is natural from the point of symmetry. The above version is NOT symmetric with respect to lo and hi. In fact, since only one splitting index is returned when two indices iand j crosses, there is no way to be symmetric! The only way to restore symmetry is creating a mirroring variant like below.
#
# code skipped here
#
        quick_sort_hoare(A, lo, p - 1)
        quick_sort_hoare(A, p, hi)
#
# code skipped here
#
    pivot = A[hi]
#
# code skipped here
#    
        if i &gt;= j:
            return i 

The posted code as in problem 7.1 of CLRS's Introduction To Algorithms, third edition is correct, too, since it is the same as your code and the code in Wikipedia. In particular, it works correctly on their example, $[13, 19, 9, 5, 12, 8, 7, 4, 11, 2, 6, 21]$. I suspect that you missed the part e of that problem, &quot;Rewrite the QUICKSORT procedure to use HOARE-PARTITION&quot;. The expected result of the rewrite will be a procedure that is just like your Python function quick_sort_hoare . In fact, that problem is written in great detail in order to prove its correctness. I would like to encourage you to go over that problem closely.