It is possible to (accidentally) lock folders in macOS so that they are read-only and protected from accidental deletion. This can happen to both local and network filestore (such as your home folder). This article shows how to resolve the issue and make the folders writable again:

You can easily see if macOS has locked a folder, by the padlock in the bottom left-hand corner of the folder icon:

To resolve the issue:

Invoke the "Get Info" dialog either by highlighting the folder and then using the keyboard shortcut "Cmd + I" or by right-clicking (or ctrl-clicking) the folder with your mouse and choosing "Get Info" from the context menu which appears:

Within the "Get Info" dialog for the folder you chose, there will be a "Locked" checkbox. Click it once to unset it:

Once you then exit the "Get Info" dialog, the folder will become (and remain) unlocked. Repeat the procedure for any other affected folders.