I think ultimately the core reason is this:
"
Shinji Kagawa is one of the best players in the world and he now plays 20 minutes at Manchester United -- on the left wing," said Klopp. "My heart breaks. Really, I have tears in my eyes."
There's a couple of other factors too, of course. I think it's upset some of the resident transfer muppets that the idea that signing a top player isn't really the simple answer to all our problems. Along with that he seems to have attracted some fanboys that take pride in relentlessly championing his cause. Then you've got the fact the main reason he's not playing in his favoured role is because of a player that most people wanted rid of in the summer. Of course there's also the issue of him being associated with many of the qualities we're lacking most at the moment (awareness of space/intelligent movement, intricate passing, creativity, pressing).
Ultimately though I think it's just the fact that we have a player in our team that is regarded by the manager, players and fans of arguably the most vibrant, exciting team in Europe as being a "world class" player and, for whatever reason, he's performing well below that level. People would just like to see him given more slack than others because he's shown he's the kind of player that can be at the heart of beautiful, exciting, title-winning football, yet at the moment it seems he's being given less slack than almost anyone in the squad.
We have a player here who the resident Dortmund (and Germany) fan believes is at a similar level to Özil and yet we're finding it hard to fit him into the team at a time when just one of our starting attackers is in good form. No-one denies that he's miles away from being in his best form but it's clear the biggest reason for that is his lack of confidence and the way we're handling him isn't likely to help that. Most players need the confidence and support of their manager to play at their best and it seems Kagawa is particularly fragile in that sense, so as much as that counts against him in terms of being "world class", it's not particularly unusual for people to think it's worth giving him that extra support.
There's a couple of myths surrounding Kagawa at the moment. As Sphaero has pointed out multiple times, Kagawa had a a reasonably long period of poor form even in his relatively short spell at Dortmund. In 10/11 by the time November came around he had just 2 goals and 2 assists in 10 league and CL starts, yet in the same period he had scored 4 goals in 5 games for Japan. So this idea that the only reason for Kagawa not being at his best at club level despite showing his quality for Japan is evidence of our blatant misuse of him is silly. The difference here is the manager stuck with him. Of course it's much easier to stick with an underperforming player when you have a small squad and the backup is Ivan Persic (now a squad player for mid-table Wolfsburg), but that show of faith led to him scoring 15 goals and getting 5 assists from then onwards as he led the march towards the league and cup double beating CL finalists Bayern in both competitions. That sort of level of performance is why people are obsessed about Kagawa. It's the kind of thing only a handful of our players have done.
The other myth is this idea that Sir Alex was giving him more and more chances as a #10 at the end of the season. It's just not true. I suppose something that ties into that myth is this idea that even when he's played out wide he's not allowed to come centrally and influence the game in the hole. The easiest way to put that particular myth to bed is simply by watching him in practically any game he plays for us there, but if that doesn't work then you can just look at his average position map v
Leverkusen and
West Brom. He's closer to the centre spot than he is to the touchline as he always is. He's playing as an inside forward as the oldies would say. In fact his proximity to the centre spot is one of the problems so far, he's dropping deep and playing nothing balls, slowing the play down and playing safe football - that's one of the issues Moyes alluded to after the match v West Brom and that kind of passive football has been a recurring theme. Regardless of that the fact is he's clearly being allowed to come centrally, if Moyes was such a stickler for rigid positions then Januzaj's movement all over the pitch would drive him mental and he'd get nowhere near the team.
Bit of a meandering post but all I'm saying is yes, Kagawa hasn't performed particularly well so far but it's not that surprising that he receives more support than our other underperforming players because a) he has qualities we're lacking at the moment that aid fluid, attacking football, b) he's proven he's capable of being a key player for a title-winning side and c) he seems to be being cut less slack than other performing players despite seemingly having a good attitude.
We basically had a 2 man midfield while City had 3 because of Nasri. No one wins 2man midfields against 3man.