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The argument goes that if there is deflation, the real interest rate rises, and so the burden on debtors increase (Paul Krugman says so in https://krugman.blogs.nytimes.com/2010/08/02/why-is-deflation-bad/).

I understand why the real rate rises, since $r = i - pi$, but why does that mean there's more of a "burden" on debtors?

If I take out a loan for 1000 dollars today, and have to pay it back a year from now, why would it affect me negatively if suddenly everything became cheaper? Sure, the money I'd be paying back (1000 dollars + interest) is "worth more", in the sense of being able to buy more stuff, but ... so what? Those 1000 dollars + interest had to be paid back no matter what. Who cares if its "worth more"? It's not my money anyways, and is due to be paid back? How exactly has my "burden" increased?

If the borrower is a firm, lower prices means your output is selling for less, so you need to sell more units in order to repay the debt (assuming a constant profit margin).

For an individual, the buried assumption is that wages are also falling in the deflation. In which case, the debt is increasing relative to your wages. However, if your wages have not fallen, falling prices will make it easier for you to repay the debt (you can consume the same amount, and have more money left over to repay debt).

It makes more sense at the macro level, as deflation is normally associated with lower growth and a higher unemployment rate.

On 1st Jan 2020, D borrows $1000 from C for one year. (So, D must repay C $1000 on 1st Jan 2021.)

Suppose that apples are the only good that is produced and consumed, and that on 1st Jan 2020, the price of each apple is $1. Then D has borrowed the equivalent of 1000 apples from C.

Suppose there is 50% deflation over the course of 2020, so that on 1st Jan 2021, the price of each apple is $0.50. Then D, who must still repay $1000, must repay the equivalent of $1000 ÷ $0.50 = 2000 apples. The cost of D's debt has gone up.

(Conversely, suppose there is 100% inflation over the course of 2020 so that on 1st Jan 2021, the price of each apple is $2. Then D, who must still repay $1000, must repay the equivalent of $1000 ÷ $2 = 500 apples. The cost of D's debt has gone down.)

In economics, the "cost" of A is ultimately the value of what you could have had if you hadn't gotten A. If you take out a loan of $1000 in 2018 and owe $1100 in 2019, then the cost of the loan is whatever $1100 buys in 2019. If it buys more in 2019, then the cost has gone up.

Another reason it can hurt debtors is if the debt is secured, meaning that there is an asset held against paying the debt. If you want to sell the asset, you find that its price fell (deflation). So it may not cover the debt.

A recent concrete example was in the United States (and other countries) in 2008. Housing prices fell. This left mortgages underwater, meaning that selling the house would not pay off the debt. People would lose the entire value of the house in foreclosure but still have left over debt.

Beyond this, even with unsecured loans, you might want to sell off assets to pay debt. But in deflation, the assets themselves have lost value.

It also may be difficult for wages to fall in deflation. But consider that wages falling can be better than the alternative: layoffs. A lower wage is often better than no wage. And in deflationary periods, layoffs are more likely than normal. Because the contracted wages may be too expensive to pay or simply because there is insufficient demand. And having to make debt payments with no income is itself difficult, making those debt holders much worse off.

Another way wages can fall is that hours might decrease. So your rate stays the same, but you get it for fewer hours, making your paycheck smaller.

That's a problem with deflation. It makes some people effectively richer (same income but lower expenses), but it makes a lot of people effectively poorer. This is particularly bad for debt holders, as the loan price often doesn't decrease (variable rate mortgages are an example of an exception).

If your source of income stays the same, then yes, it makes no difference to your debt (and lower consumption costs may leave you with more money to pay off the debt). But for many people, income does not stay the same. For those people, the debt becomes harder to service. So on average over all debt holders, the debt becomes harder to service.