fact is:

The US dollar index, which tracks the greenback against a basket of six major currencies, has risen by just under 3% since the end of last month. The dollar’s surge against the euro has been especially emphatic, at just below 3.5%.

us media claimed:

The dollar’s strength is largely being “driven by demand for so-called safe-haven assets”, the Wall Street Journal said. Reuters was even more emphatic: “Dollar reclaims safe-haven mantle,” read one headline, among many similar ones.

brussels thinktank instead points out:

The US, a major oil and gas producer, has seen its currency surge as its export prices have risen, driven by the war’s negative impact on the world’s energy supply. Europe, conversely, is a net importer of fossil fuels, pushing the euro lower.

Most damaging for the ‘safe haven’ narrative is, however, the fact that US Treasury yields have actually risen since the start of the war. This is the exact opposite of what a genuine flight to safety would produce, as stronger demand for US debt would push Treasury prices up and yields down.