Uhm... two things.
First: you see this screenshot? https://askubuntu.com/q/814380 Aside from the actual package names, the bottom part is the same kind of error I got.
See how it says "You have held __broken___ packages"?
See how the top answer is "You can use Aptitude to automatically __fix__ the __broken__ packages"?
Yeah, I interpret that to mean I had broken packages. After updating. Not before.
Oh, and actually, I think it's basically the same kind of situation as in that link. Notice it has >17k views, only 2 answers, and no accepted answer? Yeah, I guess it's not so easy to resolve.
Second: Even if I ignore the above and pretend nothing there is currently broken, a system that cannot be updated is, uhm, broken. So not only was this system just broken, it was doubly broken.