The most straightforward way to troubleshoot this would be to run a user effective access right report. Select the folder that you want to delete and go to the more actions button in the web client (the one with three vertical dots) or the Tasks menu in the Windows client. Pick Generate Report, and then select User Effective Access Rights Report. Put in your user name and then add the rights you want to run the report on (I usually just select all rights, which means that you can find any weird quirkiness).
What it will produce is a spreadsheet that looks something like this:
From there, you can determine what documents/folders you don't have sufficient access to. (It will show not only the folder you selected, but all its child documents, subfolders, their documents, etc., all the way down the line.) You can then go to the topmost item that you don't have delete rights for, and check the security on it to see what you need to grant yourself to be able to delete it.