Explanation 1: Integrate it.
Explanation 2: Imagine you're looking at an infinite TV screen that's just glowing white. If you step away, does it look any different?
Nope. What makes you think it would have a nonzero net flux? Just imagine what the setup looks like and you'll see that the flux will cancel.
Alternately just look at the Maxwell Equations (assuming that you believe in them of course). Div(B)=0.