Relevance is a part of argumentation, not a rule or container that surrounds or determines what kinds of arguments are permitted. It’s not a referee and it’s not a boundary.
Consider relevance an ask, or an indicator, that you are not doing a very good job of sharing your view with your audience/interlocutor. They are expressing that they don’t get why you are sharing what you are sharing.
It also can be an argument itself. The claim “that’s not relevant” can be an argument that generally takes the shape of “everything you are saying I have no problem with but it doesn’t advance or help your case, your side of the argument at all.” This is the expression that the information or reason is good but the entirety of the statement is out of place.
Claims to relevance are a special class of utterance in arguments and/or debates as they are opportunities for people to shore up or patch up their position in very specific ways. Too often the response to such claims is to deny them – “Of course it is relevant!” – but these defenses rely on the arguer’s perception that what they are saying makes sense. This sort of response is a bad gesture toward what was already expressed; a bad response to someone expressing doubt about a relationship of an utterance to the argument itself.
Instead of this response, consider some alternatives:
What is this argument about?
I thought we were discussing X, why don’t you think that what I said is relevant?
What are the most important issues to you related to what we are arguing about?
Chances are from these you can pretty easily see why it is that your interlocutor doesn’t see the relevance and you can either try again in an edited form or abandon it and try something else.
Another potential move here is to move to the level of the specific from the principle or vice versa. Sometimes a very specific claim or very specific story will seem to be directly relevant to you but won’t have the right uptake for someone else.
The specific to principle move sounds like: “Yea but we were talking about X which is about [principle 1, 2, 3] and this story is related in principle.”
The inverse is also useful where you make a principled claim, e.g. Rights are a poor way to protect people, something like that, and the claim of irrelevance, “What’s that got do to with anything?” – is an invitation to tell a story about an individual or some individuals.
The goal of any statement in an argument or a debate is not to try to win, but to advance the understanding of your position. A focus on winning, or taking out/down the opposition, rendering them to silence, or whatever it is people think they are doing out there eliminates opportunities for a deeper or more comprehensive understanding of the position people are taking up and their motives for doing so.
A focus on advancing understanding means you don’t throw up immediate opposition to most of these kinds of statements, but see them instead as indicators of gaps in your reasoning. Although you don’t think there are gaps in your reasoning that is highly irrelevant when you are talking to other people. They are saying these kinds of things as repair requests. Although you know you are right, they are just hearing your utterance of these familiar words for the first time. Consider it a gift when you hear such claims as they are invitations to alter your expression and keep advancing the argument by advancing your current position on it – for that too might change, or at least has the potential to change; this is the minimum required buy in to argue with anyone.
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