These are the only films that could screw Man of Steel up:
Starring Will Smith (June 7th 2013)
Starring Will Ferrell, Vince Vaughn and Owen Wilson. (June 7th 2013)
The End of the World.
Starring Seth Rogan, Jason Segal, Paul Rudd, James Franco, Michael Cera and Jonah Hill. (June 13 2013)
World War Z.
Starring Brad Pitt. (June 20th 2013)
Disney/Pixar's Monsters University
(June 20th 2013)
That, and the fact that June is the slowest box office month where many films under-perform.