It's convenient that this article and another on the nature (or lacking) of modern humility are both on the front page at the same time.
I think this entire argument reduces to a recommendation: "Humble yourself". It's so damn easy to get caught up in egocentrism. There's an intrinsic human bias towards believing that what you believe is the right thing to believe. I've never met someone who is genuinely innocent of this fault (if it can be called a fault), especially when it comes to dogmatic issues of genuine belief. It's hard to imagine what it would be like to exist as a creature that does not put its own beliefs first, of course, so I think the logic instead has to be, "yes, we may believe our own beliefs foremost, at the expense of the beliefs of others. But we must commit time to hypothetical sympathy".
To participate in an argument, we must engage in hypothetical sympathy with our counterparts. The first assumption on hearing what is perceived to be a wrong idea cannot be, "this idea is wrong, and therefore the carrier of this idea must be stupid and inferior to me, the right and correct". That turns an issue that might be argued productively into an issue of dogmatism. Most people are rational, to a functional extent. The difference lies more in the set of axioms we possess, rather than the logic used to build from them. And so we must humble ourselves; our axioms are unproveable by the definition of the word. The first step to engaging someone else is to try and imagine what set of axioms, assuming similar logic, would allow them to reach the positions they hold.
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I will note as a postscript that of course, there is a strong counterargument to this position: that there's no time for this bullshit. In an austere ivory tower, perhaps we could be humble all day, but as it stands in the real world, the lives of humans are finite, and the beliefs of some inflict real suffering. And so, most of the time it's impossible to justify this kind of gentle work towards mutual understanding. This is the perspective of arguing for the Human instead of Humanity. I don't have a good response to this other than, "damn, that's a hard one". And so, sometimes, wars are fought. I will never support their necessity, but I am sympathetic to their causes.