In short, there are some things that are risky to tell your boss. The biggest one is if you’re unhappy.
A good boss will try to work with you to resolve the issue, and help you transition to another role or company if that isn’t possible. A bad one will undermine you, violate your confidences by reporting the concern up the chain, or even outright fire you. I’ve had the all of the above happen, though it’s been a while. I think I’ve gotten better at judging people, but it’s also possible that I’ve just had a lucky streak.
It's of course a bit more elaborate, but if you feel comfortable trusting someone AND it's socially accepted that you offer it, then you are expected to offer it.
This can naturally also used to deceive people, so maybe people will act like they trust you, but doesn't while still telling you they do, so there may be people you use informal with that you don't actually trust.
But that's the general idea behind it. Nowadays, there are some, that try to use "Du" everywhere, maybe due to globalization and the proliferation of English, but this can make people (e.g. me) very uncomfortable. I then just stick with formal and in the next reply they do the same. I hate calling e.g. my boss with informal, exactly because it implies a internal trust, that just isn't there.
Mind telling more about that?