Sometimes your reader understands perfectly well what you are trying to say. Nor is the reader’s problem one of believing you after you present them with the evidence you have. No amount of evidence, in these cases, is going to persuade the reader that your claim is true. The reader has already made up their mind on a basis that is independent of the evidence you could provide. Once you make your claim you will not have time to support it. You will have to defend it.
This situation arises often in academic writing and its important not to be afraid of it. You don’t have to get your reader to believe this claim, only to accept it “for the sake of argument”. The paragraph merely has to survive the reader’s objections, so it will be your awareness of these objections that will structure the writing. You can take a hard-line view and simply try to defeat them; that is, you can try to show the reader why their prior beliefs are wrong on this matter. A softer touch involves merely convincing them that their objections to your position are not relevant in the context of your particular argument. A still softer touch is to try to show that, even if they don’t agree with you on this issue, it doesn’t undermine your larger point. The whole point of this kind of paragraph is to invite a reader that disagrees with you into the conversation. A writer who can’t tolerate disagreement isn’t much of a scholar.
Indeed, the difficulty here isn’t overcoming disagreement, but dealing with it. You are trying to position your work in a field of possible truths and you want to be aware of what might be the case, and who might be right, if you are wrong. You want to show that it wouldn’t be the end of the world; indeed, you know what the world would be like if you are. You do this by acknowledging those who take a different view of the facts. Even those who have an entirely different sense of what the facts are. Part of your reading (and therefore part of your theory) should be built out of these alternative perspectives.
But you don’t want to fall into an easy “perspectivism”. To tolerate disagreement is not to let everyone be entitled to their opinion. It requires us, for the moment, to form our own opinion and, therefore, an opinion about who is right and who is wrong about the matter at hand. Much as we admire the Dude, much as it gives us comfort to know he’s out there “taking her easy” for all us scholars, we have to look beyond the strikes and gutters, ups and downs, of the everyday hustle and bustle of our research. We’re not just swept along, from town to town like some tumbleweed in the wind. We have our reasons for believing the things we do, and we know of others who have their reasons for believing the opposite. “Live and let live,” sure. But we also know what we think.
Though we don’t get it right every time we’re not just haphazardly guessing at what it is. We’ve collected and analyzed our data very carefully and it should surprise us if we’re wrong about it. But — and here’s the important point — we are comfortable with that possibility precisely because we know that someone else, in another department (or perhaps our own), in another corner of the academy, knows the truth we missed, holds a different view of the same facts. They will pick up the slack if we are forced to abandon our current position. The truth, too, abides.