You also suggest that animal-named teams are somehow being disrespectful to the animals by having them as mascots, but that logic has a few major flaws:
1) There are teams named after humans, so aren’t we treating animals with the same respect as we’re treating other animals. I don’t see how a mascot of a Falcon is any worse than a mascot of a Patriot.
2) Team names are based on what’s tough and/or respected, not what’s despised. If team’s names were meant to be insults, there’d be teams called the Communists or the Terrorists, not the Patriots and the Cowboys.
3) You point to the fact that teams get beat down every week, but it’s the players themselves who are getting beat up. Humans are the ones directly sustaining injuries. Furthermore, whenever one team loses, another one wins. Sure the Eagles lost, but perhaps the Cardinals will be the champions, which seems to be a sign of respect toward the species of bird.