The plastics used for airplanes are a lot like reinforced concrete, where both high compression and tensile strength is needed. The plastic compound itself, polysester, vinylester, or most commonly, epoxy resin, provides the compression strength and stabilizes the fibre component, like the concrete, and the fibre component, either glass or carbon, provides most of the tensile strength, more or less like the rebar in concrete.
Like a reinforced concrete structure, the problem becomes one of how to or orient the fibre component so that the fibres can continuously carry the tensile loads. You can see right away that a resin compound by itself won't work for a high stress part; you have to have a tensile load bearing element embedded in the resin, and this load bearing element should be more or less continuous along the load path.
Random fibre segments in a resin matrix, like the chopped fibre fibreglass used in boats, won't do for something like a highly stressed beam. The fibres have to be continuous from end to end, again, a lot like a reinforced concrete beam. So this tends to rule out a process where a 3D printer could deposit resin and fibres at the same time.
It is possible to make certain aircraft parts from 3D printed plastic where the plastic by itself is replacing, say, an aluminum casting and the plastic resin is as strong, has the required hardness, and can handle the temperatures. Currently such parts would most likely be made by injection molding, 3D printing being so new. But you will certainly see lower stress casting-equivalent parts start to emerge in aviation by 3D printing, especially for low volume parts where the process is just crying for a viable application and a certifiable process. It's a conservative industry, so you have to give it time.
The challenge for now is how to make a resin matrix part, that needs high tensile strength, that can somehow be 3D printed with both the compression and tensile strength elements incorporated, and correctly oriented in the 3D print process. Not so easy.
What will probably happen in the next 10 years is someone will come up with a radical new plastic compound incorporating something like graphene in it that has all the desired properties in all directions and can be machined from a block or deposited and cured in a printing process. Then we'll have 3D printed wing spars, frames and skins.