Believe it or not when we go thru a breakup they say we go thru a six week grieving period. A break up is almost like a death and naturally we grieve that way over it. It's normal for it to hurt. All our hearts and emotions are different so for some people it takes longer than others to fully heal and move on. It all depends on the individual and how much they invested into that relationship and their partner.
What we emotionally experience with a break-up ( not speaking of the 3 week thing) is a mourning process similar to that one experiences when someone dies. Society expects us to "Just get over it" when its a break-up. We have the need to go through steps to emotionally heal; when that process is interfered with, or we allow ourselves to stay in one phase, with then we don't recover as quickly. Sum it up: we need to hurt, blame, deny, and accept.