I'm saying that under Liverpool he would thrive so the "can't cut it in the PL" narrative is rubbish. He couldn't cut it at United under Moyes and didn't perform at his best under Fergie. Which isn't surprising considering how bad United's attacking fluidity has been these last few years. This isn't some pissing contest between Kagawa and other United attacking players.
And Coutinho isn't a player miles better than Kagawa. He's playing his football under Rodgers who has transformed Liverpool's attacking football. As you said "As for Liverpool's football last season it would suit every other attacking player in a United shirt too." Just look at the difference between he and Dalglish. The goal difference between the 2012 and 2013 Liverpool sides was +24 in favor of 2013 Liverpool despite both teams being crap. A year later and the attacking football progressed even further scoring +30 more than the 2013 Liverpool side. That's the difference a manager makes. I don't think Coutinho would have done well under Moyes either. He certainly wouldn't do better than Mata.
Also what makes you think he didn't impress Van Gaal? All we know is that he didn't impress Van Gaal in the deeper midfield positions as he stated. Just because he didn't get the starting position over a better player in Mata, doesn't mean Van Gaal didn't rate him. With no Europe or league cup it makes sense for Kagawa to leave. I doubt Kagawa would have left United if Mata wasn't at United. Obviously Mata is at United and he is the better player.
Of course it is. That's how football works. Other players have out-performed Kagawa, so Kagawa has to leave.
The Liverpool stuff is entirely hypothetical anyway. I mean, we can be almost 100% certain that United players who have proven themselves competent PL performers would have done much better playing for Liverpool last season than they would have for United. Although there's an element of doubt. Kagawa
might also have been a better player under Rodgers, although the doubts about his mentality (rumours of a party-boy lifestyle, tendency to hide in tough, physical games etc.) mean we'd be a lot less certain about this.
What makes me think he didn't impress Van Gaal? The fact he couldn't find a place for him in our squad. Kagawa's biggest problem is his lack of versatility and Van Gaal likes versatile players. Not versatile enough to play more than one position, not good enough to displace better players in his position of choice and never really excelled throughout two full years of PL football under two (arguably three) different managers.
I agree entirely with your last paragraph, so not sure our opinions are all that far apart.