That's the expected behavior. The center of the view is always mapped to the center of the window (unless you play with the viewport, which I assume you don't). So if the player follows the center of the view, it always remains at the center of the window as well.
When you move the view, what should be moving is everything that doesn't move relatively to it (like a static background). If you want to see the player move, don't make him follow the view, that's simple.