Gold and the dollar have tended to move in opposite directions over long periods. The relationship is real but it works through demand rather than through any mechanical rule.
A stronger dollar raises the price elsewhere
Gold is quoted in dollars, so a buyer using another currency must first acquire dollars in order to pay for it.
When the dollar strengthens, that conversion costs more, and the metal becomes more expensive in local terms even if the dollar quote has not moved.
Physical demand outside the dollar area tends to soften in response, which reduces buying pressure on the dollar price itself.
The same forces often drive both
Rising expectations for interest rates typically strengthen the dollar by attracting capital into dollar assets.
Those same expectations raise the return available on interest bearing alternatives, which weighs on a metal that pays no income.
Much of the apparent link between the two is therefore a shared response to a third factor rather than one causing the other.
The relationship is not reliable enough to trade on
There have been extended periods when gold and the dollar rose together, usually when both were sought as refuges during international stress.
In those episodes the safe haven motive dominated the currency effect, and the usual pattern reversed for months at a time.
The correlation is therefore a tendency observed over long periods rather than a rule that holds in any particular week.
Currency indices measure only part of the picture
Common dollar indices are weighted towards a small set of developed market currencies, several of which have limited physical gold demand.
Much of the world's gold buying happens in currencies barely represented in those indices, so the index can move without reflecting what matters for demand.
A broader trade weighted measure often tells a different story from the headline index during periods when emerging market currencies are moving independently.
Local buyers experience something different
A holder outside the dollar area owns an asset whose local value combines the metal price with the exchange rate.
Where the domestic currency has been weakening, gold can rise steadily in local terms through a period when the dollar price is falling.
Reading the dollar quote as though it described everyone's experience is one of the most common misunderstandings about how the metal behaves.