The typical argument is that the value of gold is somehow super stable (often the story is brought up that in biblical times, an amount X of gold would purchase Y loaves of bread, and today it is still the same!). By contrast, the dollar lost 96% or so of its purchasing power over the last century, so clearly gold is much better, and if you tie the value of the currency to gold (=gold standard), you have the best of both worlds.

However, that story neglects many things.

1. A worker can buy many more loaves of bread (not to mention other things) with a week of wages than two thousand years ago. So, who cares about the price of gold?

2. Everyone is free to buy gold with their money, anyway, if desired [0].

3. A moderate amount of inflation is not bad, and in fact what most central banks target for, and what they have achieved for decades.

4. If you have a lot of money lying around, invest it in the markets (or into gold), don't leave it in currency.

5. A gold standard would remove the central bank's ability to control the money supply, and hamstring its ability to conduct monetary policy. Gold standard proponents consider that a feature, but almost all modern economists consider it a bug. An instructive parable is the story of the Babysitting Coop [1].

My overall take is that

good fiat > gold standard > bad fiat,

and policy should be focused on good fiat, ie keeping the central bank competent and politically independent and with a clear mandate.

[0] There have been exceptions, eg in the US in 1933, see https://en.wikipedia.org/wiki/Executive_Order_6102

[1] https://slate.com/business/1998/08/baby-sitting-the-economy....