My point though is that when teams make a move that's in the best interest of the team and not the player, fans view it as "just business", but when a player does, it's viewed as if he is selfish, arrogant, a prick, a head case, not serious about winning, etc...
That's just basic human psychology. Teams aren't a "they" to most fans, they're a "we." Being rejected by a player is, on some subrational level, a personal rejection, and humans are not, by and large, equipped to handle rejection dispassionately.
Broadly, I don't have a problem with Gauthier doing most of what he did. He's well within his rights to want to start his career early, given the limited time frame to earn money in the sport, and if he believed he had a deal in place that didn't happen, he has every right to be upset about that. However, it's not like he was an employee of the Flyers yet; until he signed that first contract, he was, for better or worse, still in the interview process, and ghosting a potential employer is immature and rude, no matter what. The mature move would have been to meet with the team, politely but firmly repeat that you don't intend to sign, and go about your business. If he had done that, then there would have been nothing to object to on either side.
As for the trade itself, we'll see how it works out, but Gauthier isn't the Flyers' problem anymore, so I'll let the Anaheim fans worry about him.