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And presuming that your own resource for attention is infinite is just wrong, trying to imitate that more so.

That's true, that's why civil discussions are so important, since you have the possibility to point out the errors in my reasoning or present sources that have not been considered by me before

Actually there's no burden on anyone, person A losing an argument against person B doesn't mean that B is right and A is wrong.

I don't agree. If opinions are stated without backing from reliable sources, they are merely opinions. Here's a paper detailing the importance of sources for viable arguments: https://www.sjsu.edu/writingcenter/docs/handouts/Argumentative%20Writing%20and%20Using%20Evidence.pdf

When two parties are in a discussion and one makes a claim that the other disputes, the one who makes the claim typically has a burden of proof to justify or substantiate that claim, especially when it challenges a perceived status quo.

Source: https://en.m.wikipedia.org/wiki/Burden_of_proof_(philosophy)