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.