I just spent 15 minutes on Apple Chat because I have been unable to highlight certain PDFs. For me, it is PDFs that contain "tables." Here is the response:
"I want to inform you that, our engineering teams are investigating an issue when opening a PDF that has two columns of texts and Preview sees it as boxes and doesn’t allow any annotations/highlights.
Workaround: In Preview, via Tools → Text Selection, or via the Markup Toolbar → Text Selection.
The current solution while this is being investigated is to edit the PDF document with a different PDF editor for macOS like Adobe Acrobat, PDF Expert, or Foxit PDF Editor but please note that these are not supported by Apple."
Their workarounds didn't work for me. Exporting to a PDF/A or printing to a PDF also didn't work. And the PDF wasn't locked or manipulated in anyway. This is a known issue.