Important Question - Are you sure this was NOT one of the system folders? No system likes that and all systems will try to stop you. You simply may not have privileges high enough. Similar problem happened to me on Widows and I ended reformatting the hard drive.
If these are YOUR files: There are few more or less drastic methods which may help, but easiest and least dangerous may be restart computer in safe mode and try there.
https://helpx.adobe.com/x-productkb/global/start-safe-boot-mode-mac.html
It should load minimum stuff in safe mode, so file may not be in use at that time. It is also worth checking the disk first from Disk Utility to make sure there are no underlying issues with the drive. And if nothing helps, it may be time to google the problem and follow some instructions. But when this happened to me in past, it was always challenge. Note, that when instructions tell you to become (and how) superuser in command line interface, you can do a LOT of damage quickly. Make VERY GOOD (and verified) backup first!