Pay attention to the scaffolding
Arguments can be divided into two parts: the main point, and “scaffolding” that you need to get that point across. The scaffolding is whatever background information is needed to explain the argument. It also typically includes many of your choices of words and examples. You may not be very interested in these words and these examples for their own sake, but need them to get the main point across.
Of course, the distinction between main points and scaffolding isn’t crisp, but it’s still useful and intuitive.
People often object to the scaffolding part of the argument. They might object to some word choice or example that you find unimportant. Sometimes these objections are unfair and a bit obnoxious. You might legitimately feel that critics should instead focus on the main point.
But even in such cases, getting a lot criticism of the scaffolding is a bit of a strategic failure on your part. You want people to discuss your main points. The scaffolding should, by definition, be inconspicuous. So if people get distracted by the scaffolding, you’ve failed to attain that goal.
But there are also cases where criticisms of the scaffolding is legitimate. In some cases, critics might correctly suspect that what you’re trying to sell as just part of the scaffolding is actually more than that. You might, for instance, use an unnecessarily politicised example in a non-political context. In such cases, objecting against that example seems legitimate. You should have used a less politicised and more inconspicuous example.
But criticisms can be legitimate even if you didn’t intentionally tried to smuggle in controversial points via the scaffolding. What’s uncontroversial and inconspicuous to you may not be so for other people, with other political views. They might feel that your choice of words was controversial or insensitive. In such cases, criticisms of the scaffolding can be legitimate, though whether that is so is a complicated issue.
I think that the originator of the argument often feels that since they initiated the discussion, it should focus on what they’re interested in - their main points. Starting to discuss the scaffolding amounts to derailing the discussion, on that view.
I think that view isn’t completely wrong, but that it’s often taken too far. Everything else equal, yes, people should focus on the original main points. But if the scaffolding contains claims that are sufficiently wrong, according to you, you can criticise them. How to weigh up these considerations is a difficult judgement.
People often don’t pay much attention to the scaffolding when they’re creating an argument. They focus on the main points, which is what they’re interested in, and create the scaffolding in a rush. But other people often feel differently: they find what you take to be mere scaffolding to be controversial and objectionable. So they’ll criticise you, rightly or wrongly, for the scaffolding, whereas you wanted to discuss your main points. To avoid that, pay attention to the scaffolding, and make sure it’s not more controversial than needed.