All babies do this - with the breastfed ones they want the breast. With the non breastfed ones they want ....a bottle....their dummy....a drink....toast....a banana...anything. Believe me, it is just as irritating when they are grizzly and wanting, regardless of how they are fed. The beauty with the breastfed ones is that you can put an end to the wanting very quickly! But, like all things, we can't always have what we want. It's OK to say no, and put a few boundaries around when it's OK and when it's not