I've stopped helping, or even started avoiding, some "friends" because of this.

Of course some tact is needed, and I've sometimes got that wrong. You have to properly listen before making suggestions, perhaps you need to ask questions first too to make sure you actually really understand, and definitely watch for signs (or explicit mentions) that advice/solutions are not wanted at this point (sometimes people just need to sound it out, to help get things in order in their own heads), and don't give definitive sounding advice when you aren't as sure as you sound, and sometimes great care needs to be given to your wording/intonation (lest advice be confused for judgement), but if after all that I make a suggestion and get my face bitten off, I am not the dick in that situation.

An actual quote, yelled before storming off: "oh, that is just like you, trying to solve everything". Damn right that is just like me, the me you know well. If someone I care about has a problem in front of me then yes I'll try help them solve it. If you don't like that, then making me not care is not particularly difficult - screaming "oh, that is just like you, trying to solve everything", storming off, and not offering any apology at all afterwards, is an effective step in that process.

Of course I need to be aware that how I react to problems may not be what other people want, and I'm not afraid to admit that empathy is a trait/skill I am sometimes not as strong in as I would like to be. But accepting that other people are different should work both ways.