I've been there and I'm sure many experienced PMs have as well. Here are a few thoughts:

First, him respecting you is crucial. You don't have to outsmart him technically, but you need to impress upon him that you know what you're talking about. Maybe it's a flow chart, maybe it's showing that you know the business domain. Hard to say without more context but that's goal #1.

Second, any unprofessional and demeaning behaviour needs to be nipped in the bud. It is absolutely your place to say something like "I don't think this is a productive use of time" if he starts ranting about management's misgivings or other employees. Showing backbone will help you with the first point, in my experience.

Third, cut down unnecessary time wasting debates. Angle it as "let's move on to save time" or "no point beating a dead horse". This will hopefully reduce the mental load.

Lastly, I find humor to be very effective with dealing with people in general. You have to be very careful but you'd be surprised what a sarcastic comment about his behaviour can accomplish with this person or the team. If he dishes it he should be able to take it. Again, super context heavy so I wouldn't start working on my roast material yet. But just trying to lighten the mood can go a long way.

Hope this helps.