One thing I frequently notice when I see an argument attempting to persuade people is that there's often a lot of inbuilt (and incorrect) assumptions about what people with opposing positions must be thinking. I think placing these assumptions in a persuasive piece, whether explicitly or implicitly, is a terrible way to go about arguing things, because there's typically going to be a wide variance in how people justify their positions and the combinations of positions they hold. There tends to be a wide variance between how a person who holds a position as a core value and a person who violently disagrees with that position thinks about it. And here I cannot stress this enough--people should want to understand why their opposition thinks the way they do.
Understanding is not equivalent to agreement, it is equivalent to knowledge. In the case of positions you know you will not agree with, its purpose is to understand the thinking of people you oppose. It's also to understand whether you truly have a strong argument for your own position. Can you respond to really clever counterattacks, or can you really only counter people whose only argument is a slogan? Not everyone needs to have a good argument for their positions, but if they don't, it might be prudent not to focus their energies on making persuasive arguments for that position. There are, after all, many ways one can forward their chosen causes besides persuasion. And really, regardless of what other possibilities for one's contributions to their chosen causes exist, it seems worthwhile to consider that botched attempts at persuasion can have exactly the opposite of the desired effect. And if this is judged to likely be the case, the best course of action is to concern oneself with using that time for anything besides persuasion instead, even if that thing has no positive impact on those causes, if it at least does not have a negative one.
Sometimes, if you carefully observe what one person says over a long period of time, you can discern the nuances of what that particular individual thinks about an issue they have discussed frequently. This cannot be used to make assumptions about what other individuals who hold the same position may think on the issue, however. It is typical that, for a given position, people from many different walks of life and perspective will hold that position. Therefore the personal experiences and motivations that lead to these different people adopting the same position can likewise be expected to differ.
This is a big reason why I think arguments should focus on the specific empirical and/or philosophical arguments being made, and not propose anything about 'how the other side thinks'.