For the sake of this question, let's consider 'argument' in a broader context, and include milder forms such as negotiation and debate.
How do I argue in an impersonal manner?
The oversimplified, yet most broadly applicable, rule is don't use any form of ad hominem. This keeps the interaction, technically, on the issue and facts.
However, you will very often find people have emotional investments in the positions they take, even one where there's little objective reason to do so. Software Developers are particularly prone to this (I encounter this at least once a week) so let's use that as a nice, safe example.
The best way I found to 'argue' in these situations is to not really argue. Instead, I plot a series of leading or probing questions to guide (fine, manipulate :) the other person to a position closer to mine.
Me: So, that's done in Trendy But Unnecessarily Complicated Framework. Cool. Do you have any guidance on how we can connect from our Boring But Everybody Knows It Just Works stack?
Them: Yeah, ok, I guess we can come up with something. Can you do Obscure Format I Read About On A Blog?
Me: Oh no, but we already support Widely Used And Proven Format, do you think that might be best for everyone?
Them: Ok, we'll talk and get back to you.
Basically, I'm asking if they agree conceptually that simple and common is 'better' without going into the emotional wilds of why they made a particular choice or why our choice is just better.
With people who I know less well...argue impersonally...don't feel like i'm arguing them, but I'm arguing the premise.
Unfortunately, this is very, very, very difficult. To the point where I would say just don't try unless you actually want a real argument. There are many things people get fixated on that are purely emotional investments and even the slightest contradiction, despite ample evidence, causes the fight or flight mechanism to kick in.
Instead, I use it as a learning (or entertainment) opportunity. You can still use probing and leading questions, just be careful to not use confrontational or challenging questions.
For example, I look forward to meeting a true Flat Earther. I know enough about the topic to be engaging but I'm really interested in their thought pattern and reasoning progression. I hold no expectation of changing their mind.
Good question: Can you explain the mechanics of constant acceleration?
Bad question: How do you reconcile your acceleration theory with centuries of empirical evidence other then a global conspiracy?