I regularly see this in chats about a subject area where I'm not the expert. The AI writes something that seems implausible, so I raise a tentative objection. "Oh, you are right, sorry" and then reverses the position on the matter. At that point, I have no idea what is right.
If I had trust in the first place, that trust would be gone. Or maybe it wouldn't, because if I had trust in the fist place, I would be gullible enough to maintain it.
The worst are areas that are dominated by layman online discussions, like say audio electronics. The AI training is full of that nonsense, and so whether your AI chatbot is a crackpot or an engineer depends entirely on what sort of language or angle you use in discussing the subject matter. It's all just a churning toilet bowl of tokens; it has no idea that the audiophile crackpot tokens and electronics engineer tokens are related and one beats the other.
You know what I mean? On the one hand, it offers to help you design the parameters for a Sallen-Key filter, asking you questions like do you want Butterworth or Chebyshev? Next minute it says nonsense like that the capacitor in a low-pass filter "bleeds high frequencies to the ground", or that a bigger filter cap in the plate supply of a tube will tighten up the bottom end for a more aggressive metal sound.
It's basically like a bar hostess who has heard enough political and economic discussions that she can catch a sentence out of a conversation and throw in a clever sounding remark. It's like that, but done at such a scale that it fools some people you used to think had their shit together.
It's just a search engine that finds garden paths through a vast amount of text, biased by the text you put in as a key. Sometimes those garden paths align with reality. The better you are able to verify whether the results are good, and/or the lower the risk if they are not, the better you are able to make use of it.
In mathematics (including information science, CS) there are all sorts of problems that are essentially searches for a solution, and many have the property that the search is computationally difficult, but verifying the solution is relatively cheap. E.g. finding integers such that a^2 + b^2 = c^2 isn't easy, but given a claim that some proposed <a, b, c> satisfies this equation is easy to check. The LLM is like that: it solves a search problem that can be fairly hard. It does so unreliably, but if you can cheaply verify the solution, there is a win there.
The remaining problems of AI are actually people problems; people causing you problems, using AI as a tool or excuse. If you get a garbage security report against your FOSS project, which wastes your time, there is an idiot person behind it, using AI for leverage. Blaming the AI, or just the AI, is a bit misplaced.