Basically pessimistic people do not like Superman and optimistic do like Superman.
Super Monkey are you saying that Byrne is a pessimist guy?
Sword of Superman are you saying that Byrne likes Superman?
I think the operating question is "Does Byrne like himself?" - or my own favorite "Does Superman like Byrne?"
I think that would be a resounding "no". And here I am, the idiot putting this on a public board.
But, onto more interesting items...
I personally agree on the pessimistic/optimistic angle. You've got to consider the viewpoint of the guy expressing the dislike. My brother, for one, used to hate Superman, favoring the X-men over him. But, then he went into Image, and all the BS dark and gritty stuff. Well, you have to ask yourself, why? Well, apparently it answers back to one's preferred state of mind. This is actually why I'm not all that interested in Marvel characters as a whole.
I like the idea of a perfect hero, I like maintaining positive but realistic ideas. So when Supes does have a flaw, a good writer involves you in it and you want him to come back out perfect again. My favorite Superman stories do that - one that comes to mind is "For the Man Who has Everything". What an appropo title to my point. Even the last days of Superman before being revised is simply perfect in that manner. Yes, I know they're both Moore, but he knows what he's doing with the character - particularly if his run on Supreme is any indication. But many Maggin stories do the same thing.
So, I consider the guy making the comments "preferred state of mind" - and that answers the question.