People sometimes believe that to make a point, it must be made once and then again for good measure. Even if the person they're making the point to is nodding or showing signs of taking on board what's being said, some people still feel inclined to labour the point again just to make sure.
This of course has a negative effect. It does little to help and more to demotivate or discourage the listener. Don't succumb to the urge to ignore a point especially when you know you are being dumped and made to understand that you are no longer special or essential to the relationship. The point to make is that you are must better off “without the dumper.”