Why don't they build airplanes from 3D printer plastic?
My assumption is that there are plastics lighter and stronger than the materials used to build planes. 


That is not a correct assumption. 

Typical 3D printer plastics have a best-case tensile strength of 45-50 MPa.
Aluminum 7075, a common aerospace alloy, has a tensile strength of 500-570 MPa.

After dividing by specific gravity, that's at a 1:4-1:5 ratio of specific strength in favor of metal. There is no significant application in which 3D printer plastics, the properties of which are driven by viscosity, adhesion, and other printing qualities, would offer better strength-to-weight than aerospace metals and fiber-reinforced composites.

Some amount of 3D-printed plastics will likely appear in cabin interiors, for low-volume parts or complex hollowed-out parts, not subjected to significant stresses. But load-bearing parts require high strength and high strength-to-weight ratio. If it's too heavy, it won't take off, and if the material's too weak, it won't stay in one piece.

So the brief answer is, they don't build airplanes from 3D printer plastic (or clay, or plaster, or thatch) because they want them to fly.