Don't really understand how Silva was more connected with the fans than Sterling was. David was famously private and quiet and never really gave interviews. He just kept his head down and stayed professional. I think the only difference between David and Raheem in terms of how much they "connected with the fans" is that David did a final goodbye video and Raheem didn't. But again, I think Silva was only happy to look back on his time with us with a tear in his eye because he was over the hill and heading back to his native land after a successful decade in England.
Raheem is still very much in his prime and isn't accepting that his time at the top is over. Where David moved a level down because his time was nearly up, Raheem's moving away to compete with us (and everyone else) for trophies.
A better comparison for Raheem would be someone like Gabby or Leroy. Players who came to us, contributed a lot in their time, and left when a better offer came along. Are you going to follow Arsenal on Twitter and hope they do well now that Gabby's there? Of course you're not. Have you hoped for Leroy to win loads and loads of titles with Bayern? Have you balls. It's easy to root for Sociedad or Anderlecht because they're smaller clubs and their fortunes will probably never affect us - the same goes for West Ham 99% of the time. Chelsea are a genuine threat to City so it's hard to feel sentimental for an ex-City player who's part of their team.
It's all perfectly understandable to feel this way, just don't try to pretend it's Raheem's fault.