Because we got spoilt by our previous generation of players. Now, am not saying Azpi is like Terry, Lampard, Drogba etc. He isn't but because he supposedly isn't screaming or seen constantly organizing the defence, he becomes an easy stick to beat with when things go around, he gets blamed because of the defensive incompetency of others. He isn't quite as consistent and flawless as he was say 2-3 years ago but he's still by far our most reliable defender. He might even feel relieved that Silva has joined!
As for the stuff Azpi does off the pitch, yeah. The club captain has lots of responsibilities off the pitch as well and if you read the news/stories, you'll notice that he does represent the club extremely well and is also well respected by the players as well as being thought highly by by our managers over the years. Only a few weeks ago, Lampard praised him at length after the Champions League game (or maybe the FA Cup final).