Direct your attention to the first line "If both of the addends have the same sign, the output must have that sign"
This is absolutely not true, as already shown.
x=5
y=10
z=x-y=-5, which has different sign from x.
If we assume sign of y inverts because of the operation, then direct your attention to the second line "However, for x−y that means if x and y have different signs the output must have the sign of x"
x=-3
y=-6=>6
these now have different sign, so result should have sign of x, but
z=x+y=3, which again has different sign from x.
This is absolutely not true, as already shown. x=5 y=10 z=x-y=-5, which has different sign from x.
If we assume sign of y inverts because of the operation, then direct your attention to the second line "However, for x−y that means if x and y have different signs the output must have the sign of x" x=-3 y=-6=>6 these now have different sign, so result should have sign of x, but z=x+y=3, which again has different sign from x.