Why did farmers in the late 1800s want inflation?
They could have sold their production for higher prices.
At the end of the nineteenth century farmers in the Midwest were very critical of the trusts and of the gold standard. The Gold Standard made inflation completely impossible. Only rich bankers could afford to have gold.
Gold Standard created deflation which lowered the benefits of farmers. Therefore it was harder and harder to pay back their original loan. If you borrow 1000 $ and you make less and less it is obvious that paying back is going to be harder. The railway companies trusts were able to impose very high prices.
The Populist Movement thus rose in opposition to that hegemony. William Jennings Bryan, a Nebraska lawyer with his "Cross of Gold" was a well-known critic of the gold standard who ran in the 1896 presidential election, one of the most crucial in American History.
Inflation would make it easier for the farmers to pay off their debts.
Farmers need to borrow large sums of money. The capital investments in land, farm machinery, and even seed in the spring require farmers to borrow larges sums of money.
The farmer needs to pay off these loans often over any where from 5 years for machinery to 20 years for land loans. The value of money affects the farmers ability to pay off the loans. If the inflation lowers the value of money it makes it easier for the farmer to pay off the loans.
For an extreme example if there was 10% inflation over five years it would cost 161.05 dollars to buy what would have cost 100 dollars to pay for five years before. Or to look at it from the other direction the value of the 100 dollars borrowed five years before is now only worth 59.04 dollars. This makes it easier for the farmer to pay off the huge sums of money that the farmer has to borrow to operate the farms.