Simplificando, é por causa da concorrência de outros filmes.
Há também uma página aqui com exatamente a mesma pergunta e chegam às mesmas conclusões:
Fox isn't speaking out on why the sequel to Independence Day is shuffling to June. So let's take a look at what could be the reason. First off might be helmer Roland Emmerich, who is nowhere near the draw he once was...
While Emmerich's shaky filmography could be a factor, what's more likely is that Fox has realized how stacked with releases July 1st, 2016 has become. That very weekend will see the release of Angry Birds, an animated movie based on the popular video game. Competing with this family friendly cartoon will be Buena Vista's adventure The BFG, an adaptation of the Roald Dahl book adapted by blockbuster god Steven Spielberg. Lastly, Warner Bros swings in with its big-budget, live-action adventure Tarzan...
Maybe this combo was too much for Fox. Now, Independence Day 2 gets a jump on all three.