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?
Answer
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.
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