The US didn't finally abandon the gold standard until the Nixon administration in 1973, when that great realist[1] recognised that the US could no longer meet its obligations in gold. Gold immediately shot up from the price of $35 an ounce that the US had held it at since the FDR administration to several hundred dollars an ounce, peaking at $800 or so in the early 'eighties (as I remember).
Between the wars various countries (including the US) went on and off the standard at various times but the system was re-established by the Bretton Woods agreement of 1944, under which countries tied their currency to the dollar, which was tied to gold at $35 an ounce, so that in effect every country subscribing to the agreement was tied to gold.
The Bretton Woods system finally fell apart in the early 'seventies, arguably because of the inflationary pressure caused by the Arab nationalisation of their oil industries.
As to why it should be abandoned - there are various possible reasons. Central to them however is the desire to issue more nominal money than you have enough gold reserves to back. Why you should want to do that is another, more complicated, story but it mostly traces back to the 'money illusion' - the delusion that if you have more money you are better off, so there is continual pressure for wages, prices, dividends, welfare benefits ... to rise.
And you can't do that on the gold standard unless you have enough gold to back it up. And gold is in finite, limited, supply.
[1] Whatever else you think of him. He had previously devalued the dollar against gold in 1971, but it only floated from 1973 (I'm pretty sure).