Why do items that are clearly payments or debits show up on a category report as 'Income'

The short answer is that the Category Summary report is an old report which will eventually be retired from the program, and it has some quirks and bugs. In this case, I'll bet you have a transaction which is in the opposite of normal direction (such as a credit for a return) that causes the Category Summary report to move the entire category from Expenses to Income.

Fortunately, there's an easy solution: recreate your report using the modern reports engine which is slowly replacing the old reports. In this case, you'd use "Create Transaction Report" on the reports menu. Set Rows=Category, click Continue to Customize, set your desired date range, and if desired, any other filters by account or category, and create the report. In this report, expense categories are always expenses, even if the total is a negative value. Also, in the new reports you can customize which columns appear in the report, re-order the columns and change their widths, a force them to fit on a single page wide when printing -- all features the old Category Summary report was lacking.

P.S. It's not your fault for not knowing about "old" versus "new" reports; the developers have done an awful job, in my opinion, of not making this more transparent to users.