In the Star Trek Universe the replicator is able to build nearly anything from clothing to a hot meal seemingly out of thin air. Creating artificial life using it and replicating a living being have been taboo subjects.
It appears that perhaps, this was an ethical line that the writers did not, or could not cross. Was there ever an in universe explanation why replicating life wasn't possible?
This is covered in the Star Trek: The Next Generation Technical Manual, considered a canon source of info about the Star Trek universe:
Because of the massive amount of computer memory required to store even the simplest object, it is impossible to record each molecule individually. Instead, extensive data compression and averaging techniques are used. Such techniques reduce memory storage required for molecular patterns by factors approaching 2.7 x 109. The resulting single-bit inaccuracies do not significantly impact the quality of most reproduced objects, but preclude the use of replicator technology to re-create living objects. Single-bit molecular errors could have severely detrimental effects on living DNA molecules and neural activity. Cumulative effects have been shown to closely resemble radiation-induced damage.
The data themselves are subject to significant accuracy limits. It is not feasible to record or store quantum electron- state information, nor can Brownian motion data be accurately re-created. Doing so would represent another billion-fold increase in the memory required to store a given pattern. This means that even if each atom of every molecule were reproduced, it is not feasible to accurately re-create the electron shell activity patterns or the atomic motions that determine the dynamics of the biochemical activity of consciousness and thought.
To re-phrase Richard's quote in simpler terms, the replicator is the end stage of 3D printing. It works by creating a form and filling the form with material. So, for example, if you want a glass of water the instructions will read like this:
create a cylinder 8cm x 12cm, 5mm thick, one end closed. 50% radius on all corners. Fill with glass at 20 degrees C. Present closed end down.
glass: SiO2, amorphous form.
create 400ml water (H20) at 5 degrees C. Put in cylinder.
It took me 2 minutes to write precise instructions to create a glass of water out of bare elements. Now picture the instructions needed to create a mouse. Sure, you can create arrays for things like hair, and bones are often mirror copies, but working organs are a different matter. Not even Star Trek computers have enough memory to keep that on file.
The transporter just moves you from place to place - it doesn't save a full specification.
If it did, we could have this scenario
