There is this thing that I've noticed happen when I'm speaking about something I've heard or read about but don't feel like an expert on. I believe that one should not spread information unless one truely understands it as well as how the information was gathered, what knowledge it builds on, what relevance and meaning it has in the context it likely will be applied in by the person who receives the information, and a few other principles that are hardly possible to honour every time. Those principles cannot be applied to everday conversations like smalltalk, without eliminating the interaction. (That's another topic, though.) So I don't apply them in general conversations with colleagues and customers and often overlook them in conversations with friends and other peers. So it is almost inevitable that I at some point say something I'm not 99.99% sure is correct the way I present it. It happens a lot with "interesting facts" and "what most people don't know". What happens then is that I feel in the wrong to some degree - because I have not made absolutely sure that I'm neither wrong nor going to be misunderstood - while the person I'm speaking to (if they see me as a peer, take me serious and are listening to me) takes what I say as new information and fits in into what they already know and believe. They don't know about the tiny feeling of guilt that I have. So I am regularly surprised when I speak to someone and seem to influence their set of beliefs inadvertently.
How to convince somebody of something is quite a complicated question psychologically. I've read enough about it to know that and to know that I'm not interested in learning how to do it in any professional way (or with style). But there are some interesting aspects to know about how easily people can change their mind in some situations and how tough it is to make somebody change their mind in others.
There was an experiment done that is often referred to in social media sometimes as an interesting bit of knowledgle and sometimes as an argument of an almost political nature, hinting at the stubbernness or irrationality of people with different beliefs (usually beliefs that deverge from the widely accepted set of scientific knowdlege). The simplified conclusion of this study is often presented as this: Presenting a person with a firm belief evidence that their belief is factually wrong makes it even stronger (see Backfire Effect). The conclusion that people draw from this sometimes is: Arguing rationally with somebody with an irrational belief will have the opposite from the intended effect. That is not usually true, though. Not only are cases where that happened rare even in the study that is referred to, the effect could also not be replicated when several researchers tried.
Sometimes I come across a person and learn of a belief of theirs that I find problematic for some reason or another. An extremist attitude to societies basic questions, fascist ideas formulated into political demands, a conspiracy narrative that results in hostile behaviour, things like that. These are usually beliefs with a large foundation that was built over years if not decades and they are often embedded in a world view that justifies and explains anything that might appear to others to oppose ethical code or the reasoning behind the belief. But "often" is not "always". And even if those things are the case is the assumption that simple, rational arguments won't have a positive effect is an erroneous one that is made too quickly. Yes, it seems like a hard undertaking to craft responses that take the opposite of your own beliefs into account properly, not as the hallucination of the enemy camp but as an equal to your own opinion. It also feels like the work necessary to formulate a response that foresees all the expectable counter-arguments and to answer all the antagonistical follow-up questions. That's the things I expect to be confronted with after objecting to something somebody said in a conversation. Correctly so. But if forging a plan to optimally convince the opponent to abandon a belief of theirs is not what I want to do, then it's not necessary to put that much work into it. You can just respond honestly with a simple thought and even end the conversation if it becomes too cumbersome. When a topic has an emotional component, it's easy to forget that keeping this on the level of a regular conversation with no expectation that it will have any meaning to anybody other than passing time.
The insight that I keep having and intend to remember in applicable situations more often is that it is not necessary but possible to convince somebody to take on a different view on something. My mind is not short of explanations and explanation attempts from opposite viewpoints and I'm ready to share them with others to encourage a broadening of their thinking. If it's my own view, a belief based on my own experience, I'm often more reluctant to share it if it opposes somebody else's belief. But it is worth it. Provided both conversing parties bring forth the necessary trust to take other's assertions seriously, a calm, rational objection is far better than cutting the topic short. The latter can easily have the same effect as saying something like "Oh, you're one of those." Derogatory remarks should be avoided just like dismissing a concern, be it ever so irrational. Ignoring an argument for being too absurd or discrediting a source without a reason, talking down or being in any way not as respectful as you would like to be treated yourself in an emotional discussion will not get you closer to invoking insight nor to learning something useful yourself. Those aren't new ideas. The realisation that is, as a conscious insight, new to me, is that I'm far more likely to influence somebody's thinking than I assumed. If a respectful discussion can't be maintained for after small talk got out of the area of the mundane, I don't need to maintain it any longer. One sincere offer of a different view on something is better than none, and better than one with a snarky remark about anti-science belief systems appended, which will likely not make your conversational partner want to think about any of what you said. Say something positive and let it sink it. The hours and even night after you talked can do a lot for making a new idea a familiar one that can or needs to be integrated with ones world view.
I will not continue to give tips on how to convince people of anything. That's not what this entry was supposed to be about. And I'm not experienced enough to give good tips. But I want to leave a book referral here. I can't recommend it, because I haven't read it. But it appears to me that Lee McIntyre knows what he's talking about in his book "How to Talk to a Science Denier". I conclude that from what he says in book introduction (YT, IV.