I've read that some of it is due to the "exit interviews" at the end of the season. Apparently Brogdon (and Gallinari) were told that they were in the Celtics long-term plans. To then find yourself on the verge of being traded, without warning, probably would make most people angry.
People quote "it's a business", but so are all of the jobs we fans have. If our bosses outright lied to us, I'm sure we'd be angry. The problem for Brogdon -- and all players, really -- is there isn't a GM out there who doesn't lie. Some may communicate better than others, but they're all going to trade a player if there's a deal that improves the team.