That sounds odd…
Try one of the following:
– Create a new user and try run FCPX under the new user
– try start OS X in safe mode and see if the app then will start
If one of the above fixes your problem you have a problem with a third party application on you system. Now you have to zero in on that application (which can be hard).
It it doesn’t work I would do a complete uninstall of the FCPX by using something like ‘AppZapper’ which completely removes (*zap*) the app, settings, etc. And the make a complete reinstall of the app.
The last step is to make a clean installation of your OS X