Unsolicited advice is generally offensive. If they wanted your advice on how to fix their problems they would ask you. If they don't and you go ahead anyway then you imply that you are superior to them and just come off as obnoxious.
It is not generally offensive to offer a suggestion about how to solve a problem, what's offensive is abusing people time by rehearsing the same complaints over and over again while ignoring any kind of solution. If they whine constantly about a problem but never seek any way to solve it, it is just attention-seeking behavior.
>If they don't and you go ahead anyway then you imply that you are superior to them and just come off as obnoxious.
No. It implies that the person has already had the problem and solved it successfully or they have the knowledge to solve it successfully or they are trying to brainstorm what they would do.
From my experience the perception is usually rather negative. I think the reason for this is it's hard to impossible to have the full context which can include effort spent already on something as well as actual need and other information that is just not available to the other person.
I know a lot of construction workers and lawyers (for some reason), and while lawyers like a good argument (and backstabbing) off client time, neither of the groups likes problem solving or doing the professional version outside of being paid for it. Well, except for some (usually broke) newbies anyway.