This is from my own personal experience having these conversations, both as the white person in question, and as the white guy looking at this other white person like "dude, no, wait."
Discussions about race relations with some white people break down because sometimes, a white person is already holding a self-congratulatory position for having decided to engage at all. And they will be waiting for either outright, or more subtle, acknowledgement of that generosity.
If you do not reward that white person for allowing themselves to be placed in a vulnerable position when they didn't have to, they will close down and begin retaliating and pointing out the lack of tolerance being shown them and their suggestions.
A lot of white people really just want to be reassured while they're messing up that even with these demerits on their record, they're still one of the good ones. Because they know they're one of the good ones, down deep, and if you can't be trusted to recognize that, how the hell can you be trusted to exchange ideas in good faith?
So before you can challenge their beliefs and their worldview, you have to make sure that somewhere in the initial discussion period, you give them propers for even coming to the table. Once you do that, you're free to continue and even criticize, now that they are safe in their knowledge they're one of the good ones.
They will shut down if told they're one of the bad ones. But if you're telling them they're a good one, but here's how you become a better one, then they're all good.
Again: I've been this dude before. I've seen this guy since. I've talked to this guy, and as annoying as it may be, most of the time any progress made is made because I made sure to reassure the guy that he had not stepped outside of his bubble in vain, and that I understood him and where he was coming from.
It's some handholdy shit, for sure. Which makes usage of terms like "snowflake" and "participation trophy" that much harder to let go when they inevitably pop out.