Maybe we just see things differently, but I just feel like calling him an arrogant narcissist is just way too far given what I've seen. I could understand it if you said him holding up the trophy was a bit self-indulgent. Personally I'd give him a pass since his team just won nationals, and I think every NP kid there was fine with it, but I'd understand where you're coming from.
That said, I think concluding someone is an arrogant narcissist because they celebrated with their team after finding out they won nationals is a real stretch. I feel like I can just explain that behavior as him being caught up in the moment because he just found out they won nationals. In my mind, that's an incredibly normal human reaction to achieving a goal you've worked hard on, so I don't know why people take everything he does and take the absolute worst interpretation they can.
Just take a hypothetical: Someone asks Brosnan what makes the team special, and Brosnan says "My kids have complete faith in me and my training, and we focus on the small things that other schools don't. Things like nutrition, injury prevention, and recovery. Our workouts aren't that different from what other schools do, but we focus on hitting the correct paces. I put in a lot of work too, more than most other HS coaches, sometimes I'll hold 2 practices a day so that everyone can make it to the workout, and I'm always refining my training and trying to learn. Culture is really important too, when I was starting, I had to drive around and make sure kids weren't goofing off. I have to thank John Doe, because he was the first guy to really buy into my coaching, and he went from 10:00 to 9:20, and he showed the rest of my guys what was possible, and he held them accountable."
When I see that, I think "Wow, all of that is incredibly true. Kids buying into a system and trusting their coach is absolutely vital for building a good team. I'm glad he didn't just talk about how talented they are, because that's not helpful in any way to someone trying to build a program. If more people took this advice and focused more on hitting the right paces, recovering well, fueling, etc, we could have a ton of really strong programs, even if there aren't 4 guys under 4:02 on every team."
For everyone here that hates Brosnan, I think you'd look at that, and say "Wow, this guy always makes everything about himself. He was asked what makes his team special, and he didn't even mention that his team is super talented. Even when he talked about the kids, he was just giving them credit for listening to him." We're taking the same information, but you just put it through the most toxic lens possible.