Now you might ask why the Fed targets 2% and not 0% and that's because a world where inflation is 0% is brutal for debtors which is basically everyone. The fact that inflations occurs basically guarantees that people who don't over leverage won't be stuck in perpetual debt. That means people can take out loans, start companies and buy equipment to grow the economy. If we had 0% inflation all of that activity becomes much harder.
Another way to see it is:
If you have mortgage inflation comes of the liability of that debt since inflation is not just inflating all the bad parts but all the parts of the economy. And de-risks investment mostly because debt is in nominal terms. Now you cannot have rabid inflation but its not just as though anything above 0% inflation is bad.