Might be a plugin or extension preventing you from being able to quit Safari ...
From your Safari menu bar click Safari > Preferences then select the Security tab.
Deselect: Allow all other plug-ins. Quit and relaunch Safari to test.
If that made a difference, instructions for troubleshooting plugins here.
If it's not a plug-in issue, select the Extensions tab. If there are any extensions installed, turn that OFF, quit and relaunch Safari to test. If that made a difference, uninstall one at a time, quit and relaunch Safari to test until you find the culprit.