Take an integer value x. Flip the sign bit. Do you now have the value -x? On a 2s complement architecture, you do not. In 2s complement, you have to flip all the bits and add one to get -x.
If you flip the sign bit, the sign changes. It does not mean that if you flip the sign, the value is negated.
If you flip the sign bit, the sign changes. It does not mean that if you flip the sign, the value is negated.