16" is either the diameter or radius, and if you have 2 halves, they still fit inside the whole circle. And if they fit inside the whole circle they won't exceed its boundaries. But the whole circle will always have areas that the 2 smaller circles won't cover, making it bigger than the 2 combined.

think about yin and yang, basically 2 circles next to eachother, both having a diameter that is half the size of the big circle they find themselves in. But you can see that the 2 circles don't cover the whole surface of the big circle.