The necessity for me is that I want clarification or remedy to what's going to irk me to no end. I fail to understand how it is arrogance just wanting someone to not sound confusing, off kilter or that I prefer them to better sound like they have full knowledge and sense in what they're talking about. I already worry about making mistakes or being mistaken. If someone is barking at me and just spouting falsities or nothing of consistent logic, I'm not just going to blindly believe them and/or fulfill whatever demands they may have. Furthermore, I will not let their wrongs become in any way, shape or form what turn me into being wrong because I just blindly followed their orders like an ignorant lemming. Likewise, if I see or hear of the same person trying to convince or convert others to their non-logic, I'm going to call that out, too. I must strongly contend against your claim that it's arrogant to make efforts preventing any amount of what would be "stupidity" in this world.
Now, per the aspect of someone yelling at me, nonsense or not, no matter their age or authority, they are just promoting their lacking confidence / faith in themselves and/or whatever they believe in. Sensationalism has never once swayed me to think that someone is smarter or better than anyone calmly having a discussion, making the same points (right or wrong).
You do you. They do them.
If they sound confusing, then let them be confused. What they say may seem perfectly logical within their value system and experience. You do not share or understand their value system and experience. (Even if you think you do, you don't.)
If it is important, say,
hold on there, I'm confused. Let's take this step by step. And confirm each step. (That's known as the "Socratic method.") If it isn't important, let... it... go. Telling them
they are confused will always be interpreted as arrogance.
Somehow, you've gone from correcting people who say something you think is incorrect to blindly following orders and fulfilling demands. That's a big jump.
If someone has the legal authority to
order you to do something, you may calmly say,
I don't think that will work out well, and here is why. That turns it into a cooperative venture and not a confrontation. Negotiation may be possible. If they pull rank (
Shut up and do it because I said so.), there may be a higher authority to appeal to. (Orders to do something illegal are invalid.)
If not, either do it or accept the consequences. Complaining only worsens your situation and adds unneeded stress. Complaints are ineffective against order-givers and only serve to anger them.
By "authority," I mean a legally recognizable ability to bring negative consequences if you don't comply. This includes parents, teachers, employers, military commanders, law enforcement, and others. A teacher may be limited to getting you expelled, while a police officer may arrest you, beat you, or kill you. Think carefully about the potential cost/benefit ratio before outright refusing to comply.
If they lack authority and it is something you won't do as a favor, then just say (as nicely as possible)
Nope. Not going to do it. And walk away. Only explain "why" if they were nice about the request and asked. They may be open to negotiation. Otherwise,
I don't want to, is all the justification you need.
There are benefits to a calm, nonconfrontational discussion. There are only negatives to an argument. You don't have to respond in kind if they decide to argue.