Why won't Preview allow changes to PDF?

I downloaded my own Chase credit card statement for last month and opened it with Preview (pdf file). I used Tools to "annotate" (selected Text tool and put the word "Testing" in red text annotation in the statement) and then Preview flashed something at the top of the window "this file cannot be modified so your changes are being saved in a copy." I then went to the File menu and selected Export as PDF ... and saved the modified (commented) version with the word "copy" appended to the original file name. Preview repeated its warnings that the original file cannot be modified but I had no problem saving my "copy" with my annotations. I was able to open and modify the "copy" version repeatedly after that. The original could not be modified.

I would show you the original and annotated versions in snapshots here but of course will not since it has my credit card info!

Is this what you are trying to do?

Boot into Safe Mode according to Start up your Mac in safe mode - Apple Support and see if you can edit and annotate one of the problem PDF files from there. Reboot normally and check again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files