As far as I can tell the problem with Superman in a nut shell.
The character is suppose to represent the something akin to a boyscout with superpowers. This idea of a humble, good man who has untold power and uses it for the betterment of mankind. A personification of what America saw itself as in the world: A world power with home grown morality and roots.
As the character aged in comics, they explored the morality. One topic touched on a lot was the guilt that such responsibility would induce. Superman is almost always depicted as holding back because he is aware of this strength and that it can hurt others. That boyscout mentality never left the character through this and instead just because a way to explore new topics, such as how he would deal with collateral damage, challenges he couldn't overcome (though would later with help because comic logic), the limits to his capacity to be everywhere at once and other things. The morality stayed pretty consistent, with a strong opposition to killing, and a selflessness if the alternative meant innocents hurt. Even the stories whee it was a "needs of the many" scenario, it would dwell on how that torn him up inside. This core, which was always suppose to be taught and engrained in him like America itself believed it ingrained it onto all it's good youths, rarely faltered unless you had poor writers behind the wheel. (most any time superman appears as a means to show how bad ass batman is, Frank miller).
The movie however seemed to paint superman as someone who casts that aside in a super hissyfit. Yes, one can argue the morality of the action. Yes one can try to explain it as an inexperienced superman's mistake that he will learn from. But to many fans, that is going too far backwards. That is not just rewriting the character, not just retreading ground that was old 5 decades ago, but betraying the core morality the character had fairly consistently within his own universe. People get mad anytime some asshole writes Sups as a government lackey, this is the same sort of, hate to put it this way, betrayal of expectations of the fans. At least that was how I understood it.
It wasn't even the destruction or the scale so much as how the character was put in the situation and reacted. How hard would it have been to even throw a scene in there where he tells someone to evacuate the place, or show a seen of people fleeing? Yes, that would be unrealistic, but this is a comic book movie, and even beyond that, this is the guy referred to as the "Big Blue Boyscout". The humble and wholesome persona. Going ape shit and causing (not just being knocked into it) as much collateral damage as was done just feels wrong to fans of superman for so long. Hell, often a villain uses his selflessness as a means to get a leg up, knowing he will try to save the people first, worry about the fight later.
So, from all of that the movie really seemed to sell out the character's character for the sake of more excessive explosions and destruction ala Transformer movies. Not surprised by backlash to be honest.