Most plastics consist of long molecules (polymer chains) intertwined like a wad of thread or cotton. When you push two wads of cotton together, they won't just stick. Same thing happens with plastics.
Additionally, the same thing applies to plastics as does to metals: the contact is not flat enough at the atomic level. However, with plastics you can improve this significantly by heating the object until it flows easily. If you push two pieces of heated plastic together, they stick reasonably well. The plasticity allows for very close contact at the molecular level, but the bond is not as strong as the plastic itself because the molecules still don't really intertwine very well.