Inflation can cause unemployment because it reduces people's buying power lowering demand.
If you control Inflation then you control unemployment.
Unemployment is a red herring. If you employed every last person in the U.S. in the military as a soldier, there would be no unemployment, but there would also be nothing to eat. Just because people are unemployed doesn't mean progress hasn't been made. When the first farming tools were made, unemployment increased because all of a sudden you don't need as many farmers, but eventually more labor went to other disciplines that hadn't been explored before and not only did wealth increase because farming was more efficient, but then things like medicine could develop which saved lives allowing more surplus labor to explore more disciplines. Unemployment is the result of economic events such as crashes or technological advances. Unemployment does not in and of itself cause economic failure. Inflation on the other hand destroys value by debasing fiat currency and ultimately distorts incentives such as those related to consumer spending and investment. Skewed incentives in investment can be particularly disastrous as the capital structure of an economy is the key to whether or not the people and businesses will be able to satisfy their value preferences, if the capital structure is distorted, oddities like buying stock on margin and lending circles appear which inevitably crash when people start saving again. There's loads of information about this at the Mises Institute.
I inflation is bad for wage workers.