> "Do you want my advice" = I know how to solve it, but maybe you don't (because you are incompetent, insecure, or not ready to know the "truth") want to solve it and it's okay for you to stay with your problems, your loss, I'm out.

No, that's not what that means.

Sure, some oversensitive people will interpret it that way. That's why I provided two other ways of asking the question. "Do you want my advice?" is okay for a lot of people, though; not everyone is so sensitive they'll take offense to that.

It has to be a question, though. And really, if someone is going to assume you think they're incompetent because you ask if they want advice, you think they won't assume you'll think they're incompetent when you say, "I think one of the possible courses of action is..."?