I am mean the situation is a bit more nuanced than that, but this is a good place to start.
I am an Everton fan, not a Moyes fan, so if he does go then I will be hoping for better but it is just far too risky, in my opinion to let him go, just yet.
There is no valid reason other than fans don't like his style of play, or don't like him.
Realistically we have probably improved more than I thought we would and this might be the consensus, if you look at predictions pre-season. There is a case that it is simply a personality clash and nothing to do with the football. Or, it is just people wanting to whinge. I would not be surprised to hear the same arguments, against him, if we were sitting in the top 4.
Are there better managers out there, in our range, of course there are. Some times though it is a case of careful what you wish for.
He has come in for stability, I don't think we can definitely say we are stable yet. We have hit calmer waters, for sure, but one more summer transfer window, another run at Europe (which we may already get this season) and then it will more realistic to judge after that. Then we can get one of these new up and coming managers in with a solid recruitment system in place.