> He directly says he's waiting to see softening of the labor market before stopping the rate hikes
Yes, because we don’t want to ruin the labor market. Right now, rates can be raised without spiking unemployment. The Fed is trying to estimate when that stops happening.
A clear signal that the limit has been reached is the labor market actually softening. That doesn’t mean the Fed is trying to raise unemployment. It’s trying to lower inflation, and thinks unemployment may rise as a result of that, though to date it has not.