safari quit and won't open

Reboot your Mac and see if the problem is cleared. If rebooting your Mac doesn’t fix things, see if the problem still happens in Safe mode (hold the shift key down at startup). It can take much longer to safe boot (10 min) so be patient.

How to use safe mode on your Mac - Apple Support 

Safe mode forces the OS to clear certain caches and logs and do other miscellaneous housekeeping. It's non-destructive to user data so is safe to do. Very often certain weird software behavior is corrected by simply logging in this way as a troubleshooting method. When you're in safe boot, the machine will not be at its best performance, especially with graphics, but that's expected.

Does the problem persist while in Safe mode?

Exit safe mode by restarting your Mac normally and re-evaluate the issue again.

If the problem is still unresolved, please return here and post a reply and we’ll see what else we can come up with for help.

a10_warcat Said:

"After following the directions above, the problem still remains unresolved."

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Reinstall the macOS:

Nothing would be deleted. It's just that items that have become corrupted or deleted, would be replaced or reinstalled back to where they should be. Go Here: How to reinstall macOS from macOS Recovery - Apple Support. Important: Be certain to create a backup of your Mac prior to all of this. That way, you can have something to restore from the Mac from, should anything go wrong with the reinstall.

deborafromvictorville Said:

"safari quit and won't open, what do I do"

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Refer to the link provided atop this post..

After following the directions above, the problem still remains unresolved.