If you can't delete the user for some reason, you can remove it at the command line.
Launch "Terminal" (from /Applications/Utilities/Terminal.app, or search via Spotlight) and type:
sudo dscl . list /Users
...followed by your administrator password. Then hit enter
The output will show you the shortname of your local users (towards the bottom).
Here I called the user to be removed "testy" (I'm only showing the last few entries):
Now remove the user from your system and from System Preferences (exchanging the shortname "testy" with your own, found earlier):
sudo dscl . delete /Users/testy
Then hit enter.
The home folder of that user you can either keep, if there are important files, or delete it with...
sudo rm -r /Users/testy
...and again hit enter.
PS. A speculative answer for the permissions error received and mentioned in the comments section can be found at StackExchange:
What causes eDSPermissionError when running dscl?