I don't have a lot of unreasonable hatred for the Patriots. My only animosity comes from:
a. They were the team that the Chargers were playing last year in the playoffs that won because we totally gave the game away. There were numerous blunders made by the Chargers that totally changed the outcome, and we only lost by 3 points. To add to that, they were arrogant and disrespectful at the end of the game. It was bad enough to lose that way, then to add their unsportsmanlike conduct just made it worse. I think this is a valid reason to dislike a team.
b. The whole cheating thing. As a fan I have no idea how widespread that type of thing is, but regardless, they got caught. I think it's just despicable. I believe this is a valid reson to dislike them.
I don't take it to the extreme in hoping for injuries or anything like that, it's just a football preference for me. Similar to disliking the Giants these days because Eli Manning, who was drafted by the Chargers, refused to play in San Diego. What a flippin whiner! I like the result of that, as we got Rivers and a couple of draft picks, which turned out to be Shawne Merriman and Nate Kaeding (great place kicker), and we didn't have to have Eli Manning as QB. At the time Rivers was sitting behing Drew Breese, but at this point Rivers is clearly better that Eli.