Final Cut Pro X crashes when first opened

Whenever the application crashes, its plist file tends to get corrupted, and this in turn causes more crashes.

To delete preferences, hold down command and option while starting the application and click Delete Custom Settings. The application will start with default settings and open an “Untitled” library. Adjust the settings, reopen the library you were working, and see how it works now.

Also, if you are not using the current version, 11.2, consider updating. Make a zip of your existing version, just in case, and update at the App Store.

In addition to the always excellent advice from Luis, it's also possible the library that is automatically opened is corrupt. If you launch FCP while holding the option key, it will ask which library you want to open. Choose a different library or create a new one and see if FCP behaves better.