Well, for one, people get tired of the same team always winning (call it envy, if you want), and after they won three Super Bowls in four years, people had had enough of them. Add in Bill Belichick being a dick and a poor sport, which doesn't come across well as the face of the franchise, plus Spygate, and it is easy to see why a lot of people dislike the Patriots.
It is cool that they did the jersey trade thing, but let's not kid ourselves: a large part of it was selfish, as they don't want their organization associated with a possible murderer anymore, and they don't want fans showing up to games wearing their Patriots Hernandez jerseys, so offering a new one for his old one is a way of vastly decreasing the number of Hernandez jerseys that will be seen at future Patriots home games. Still a nice gesture, for sure, but it wasn't totally selfless.