Agree entirely, you seem like a sound bloke btw.
Ange is prickly and clearly has an issue with people who disagree with him. I work in an environment where disagreement and criticism are fundamental, so when someone disagrees with me or offers straight feedback I see it as an opportunity to learn and develop, I don't double down and assume only I have the correct answers to doing things. We all have different specialisms and skills and learning from other people is key to our growth.
The impression I get with Ange is someone thin-skinned, kind of aggressive, who can be charming when things are going their way. When it's a bit more difficult there's a nasty side that comes out quite quickly. He's made a rod for his own back with his confrontational approach and in football when you take on the fans that's always a bad thing: that doesn't make abusing him ok, of course not, but it's not hard to see why you might be offered some quite 'direct' criticism as a result of that approach.
Anyway, tl;dr: don't take on the baying mob, there's nothing to be gained from that situation, an intelligent person realises you steer clear.