Answer:
Being that the government is supposed to protect its citizens no matter what the cost, it may seem a little counterintuitive for them to hide information from us regarding our own military's involvement with other countries. Sure, maybe they don't want prescious info getting out to the wrong people, but it's generally our right as citizens to know what our government is doing. This is precisely why the protection for freedom of speech is so important, because if our own government isn't going to inform us about their activities, then who will?
In the case of the New York Times publishing secret/classified government papers, they are excersizing their right of freedom of speech/freedom of the press, in order to inform the general public of the government's actions. This intern allows the people to feel like they're "in the loop", and thus strengthens the relationship between the government and its people.
Explanation:
Essentially the protection for freedom of speech/press is important, because it allows us, as citizens, to share information about our government, that it may not be able to share with us.
Hope this helps :)