Let us continue to use the pseudo instruction:
The sign flag indicates whether the difference of a subtraction is negative or not, but it cannot be used to indicate whether x > y when both numbers are interpreted signed.
As an exercise, try the following combinations (use the 4-bit system to make things simpler). First, figure out the bit patterns for each value. Then carry out the binary subtraction and determine the MSb of the result.
x = 0,y = -1,S = 1,x > y.
x = 7,y = -8,S = 0,x > y.
Because the sign flag has different values in two comparisons that should have the same conclusion, the sign flag, at least by itself, cannot be used to indicate the result of a comparison of signed numbers.