Agree. There is a simple rule I learned in economics class: The higher inflation is the lower unemployement will be, the lower inflation is the higher unemployment will be. We don't want too much of either, but given the choice I would prefer to control inflation, as high inflation ultimately does far more damage to the economy in the long term.
Unfortunately, the rule you leaned is clasical Keynesian economics. It has been shown to have exceptions in modern economies, particularly in the 1970's. See for example stagflation.
Well, I did forget to mention that the rule only applies in the short term. No economic rule is perfect anyways, they are very general, and can't account for all factors.
Or, conversely, the 1990's, in which inflation and unemployment were both low.
The key is keeping the economy running at maximum productivity. Unemployment is thus bad, because it represents inefficiency in the economy; every person who doesn't have a job is someone who is not contributing, but yet they still must consume resources in order to survive. Consumption has to be met by productivity.
Clearly run away inflation is a bad thing, but as long as everyone is working in a job in which they are producing either a valuable good or providing a valuable service, and are being compensated fairly for it, it will be kept in check. The key is to ensure that consumption and production of goods is kept in balance.