Reason behind Man of Steels muted tones

^{The following is just a first start, not so much based on proper quotes from the responsible film-makers rather than common sense and the respective Wikipedia article on the movie.}

First and foremost the visual style of a movie is to a large degree up to its director and Zack Snyder has repeatedly shown his affinity towards darker and gloomier color tones, even if Man of Steel is still a bit more "conventionally" colored than say 300, Sucker Punch or even Watchmen. But I guess you can see where he comes from. Add to this, that this style imbues the whole movie and not just individual scenes in order to give it a coherent style throughout the whole picture, fitting to its rather dark themes and overall emotional tone.

Which brings us to its relevance for the movie's story and its themes. The general idea of Man of Steel as yet another reboot of Superman was primarily to go into a darker and more realistic (or upto cynical) direction with it. This was primarily based on two things, the rather low critical and financial success of Superman Returns, which was held in a very nostalgic (one might even say "misty-eyed") style, regarding both the general story and its filmic interpretation. And on the other hand you have the big critical and financial success of Christopher Nolan's very realistic and dark reimagining of Batman. So while a crossover between Superman and Batman might not have been immediately in mind at that time, the Batman reboot and its success was still a big motivation to go into a similar line with the new Superman (and afterall Nolan still worked as a producer on Man of Steel and developed the general idea together with screenwriter David S. Goyer, who already worked with him on his Batman series).

And part of this darker and gloomier reimagining of all the DC properties is probably also based on the fact that their biggest competitor, Marvel, has great success with pretty much the opposite direction. So a repositioning of their properties as a contrast to Marvel's funny, colorful and lighthearted movies might also serve to find a proper niche for their films instead of simply copying their competitors. (And even as a total comic-ignoramus I always got the impression that this contrast between lightheartedness and a darker attitude was also inherent in Marvel's and DC's respective comic properties in the first place).

I do not think the movie was "very dark and gloomy". No way. That's your personal perception and it is not how I or many others perceived it. Have you seen Lord of the Rings? Most of their movies were "very dark and gloomy", I agree with that. Man of Steel had muted tones, that's right, but not dark and gloomy. The movie had steel colours. It was a perfect balance between the colour of steel, which resonates with the title of the movie, the main character's personality and the sad events pictured in the movie i.e. the destruction of Krypton and Earth too being on the verge of disappearance.

So it wasn't dark and gloomy, it was steely.