How come the US dollar strengthened versus other currencies while weakening against itself?
Weakening against itself is an absolute measure. More dollars absolutely means that each one is worth less.
However, strengthening versus other currencies is relative. There were two factors that made the US dollar relatively more attractive:
(1) Inflation creates instability, and instability pushes investors towards lower risk. Many deem the US dollar to be the lowest risk currency. So, as always happens when there is economic turmoil, the recent bout of inflation increased the relative demand for US dollars.
(2) Inflation in other countries tended to lag the US by several months, which meant that the US was the first country to rapidly increase interest rates. Higher interest rates meant that the US became a more attractive place to park cash, hence an increased relative demand for dollars
.Thank you to the excellent Ellery Fisher for prompting this topic!