Instead assuming good faith - you and I are no oracles. Even our strongest arguments will have gaps, things we hadn't considered. Our arguments will sometimes have flaws - incorrect assumptions or other faulty basis we hadn't realized we'd made. It's the cost of being human.
It's not so much certainty of belief, but being able to move forward with confidence, and argue for, the best path you can discern - yet aware that even the best of us will be wrong at least some of the time. It's about being able to recognize and turn on a dime - to course correct - when that stronger argument is made for a different path, even if you were damn sure about the one you were on not a moment before.
[1] EDIT: Err, arguing only for the side you don't believe in at any rate. Arguing for both sides or explicitly playing devil's advocate if the other party seems to be arguing your own viewpoint sufficiently seems perfectly fine though.
As somebody slightly on the autistic spectrum, I find it hard to understand why a lot of people don't operate like this.
There is of course a difference between factual information and emotional response or differences in taste; I assume this discussion is only about empirical facts and not personal preference.
Against this, you might pit an ideal bayesian reasoner tracking a degree of belief in all possibilities. But that's too hard. It is possible for humans to roughly track a few possibilities; if you pick simple ones, none will be exactly right, but you can learn from how they go wrong or not. It's like "try the simplest thing that can possibly work" in programming: you expect there's a good chance it won't, but it can be the most productive way forward to figuring out what will.
"When my information changes, I change my mind. What do you do?"
"What, probably, more than anything else marks the true leader is the power to clench his teeth and hang on, the ability to impart to others a confidence that he feels himself. This he can do only if he does feel it. Never, until the very last moment, must he despair of his own genius. Above all, he must be willing to accept for the men under him, no less than for himself, sacrifices which may be productive of good, rather than a shameful yielding which must remain for ever useless" - Marc Bloch "Strange Defeat"
This quote really hit me because I have been thinking about my own failures as a leader and as a businessperson; I approached leadership as you would approach a technician job. Honesty is important. Openness to new ideas is important. Humility is pleasant. Confidence is irrelevant.
It is great for a technician to say "I'm happy to do everything I can to make the project at hand succeed. I see it as my responsibility, though, to tell you that it will probably fail anyhow, for these reasons."
That makes you a good technician; But a bad leader. It's interesting, because I think that you are a bad technician if you act like a leader and show confidence when the chances don't warrant that confidence. You are, then, lying, and while people will follow a lying leader to the end of the earth, if s/he is good enough at it, a lying technician is nothing but a liability. A lying technician is worth less than nothing. A lot less.
Leaders, of course, have been selected for and trained for leadership, so they are attuned to those qualities. They end up picking confidence and other leadership qualities over honesty, humility an other technician qualities, even when they pick technicians. This is one of the big reasons why I thought I could be a leader, and one of the reasons I was able to pay my rent in that role, even though I couldn't approach opportunity cost profitability... I really am way better at selecting technicians than someone who thinks like a manager usually is, mostly because I don't give points for confidence. Unfortunately, that is only one aspect of management, one that is not particularly profitable on it's own.
I personally think that as a technician, the best way to handle this, the best way to project confidence to the boss while still maintaining the honesty and humility required is to always act confident around the boss, because otherwise they won't listen to you, but then to give percentages "I'm 65% certain that solution Z will solve the problem at hand" - that way you maintain the actual honesty, while still projecting the confidence that some bosses require.