Maybe the reason why people keep repeating it is because that's more or less what Powell keeps saying: "Reducing inflation will likely require a sustained period of below-trend growth, and it will very likely require a softening of labor conditions," (source:
https://www.cbsnews.com/news/federal-reserve-interest-rate-h...)
Softening of labor conditions is pretty directly saying "Increase unemployment".
> and why cuts are so cautious.
They're so cautious because they want to hit the right amount of increased unemployment, not that they don't want unemployment to go up at all.