First, a brief introduction to the concept for the uninitiated - 12 tone music, in it's simplest form, is created from a 'row' -- a random sequence of notes, each one different from any previous until all 12 notes of the chromatic scale have been used up. There are a few basic rules - use notes in your composition in the sequence they appear in the row. No note may be repeated until all other notes in the sequence have been used. The rhythm and duration of each note can be freely assigned. Notes may appear in any octave. The composer is free to apply any additional constraints as desired.
Advanced techniques include inverting the row -- starting with the same pitch as the original row, except moving through the row inverting the intervals. For example, if the first note of a row is G, and the second is B-flat (up a minor third), the inverted row would start with G, and it's second note would be E (down a minor third), and so on and so forth. A retrograde row would simply start with the last note of the row and proceed to the first. Then there's the retrograde inversion. You get the picture...
This is not a new technique. It has been around since 'popularized' by Arnold Schoenberg near the beginning of the last century, almost a hundred years ago, now. Always controversial, the music created using this technique ranges from quite listenable to unintelligible. The problem, I believe, is with the perception of would be composers that the rules and random nature of the technique absolve them from responsibility for the ultimate outcome.
Similar restrictive techniques have been applied to other art media, again with mixed results. Assemble any panel of 'artists' and present them with a random collection of refuse from the local landfill, and you will be greeted with a wide range of artistic expressions, ranging from re-arranged piles of refuse to the truly artistic interpretation and expression of feeling and meaning. A gifted and inspired artist creates a work that transcends the material media and raises our perceptions beyond the physical. No matter how soft and fanciful she looks, The Little Mermaid is actually a chunk of metal sitting on a rock. Hmmm.... somehow I never thought of it that way until this very moment. The art transcends the medium.
The twelve tone row is a pile of musical refuse, a rigid and seemingly inflexible mold. It pushes back. It wields an imposing influence on the process. Lesser composers bend under the pressure. They make excuses for the medium. They allow the material and the tools to take the foreground of their expression. Their art does not transcend or inspire. When asked why their music sounds so terrible their response is, "it's supposed to sound that way. It's 12 tone."
Don't buy it. Too often, the unskilled or the incompetent hide behind the guise of '12 tone' music. "Why yes, I'm a composer! Look what I wrote!" The intent of the 12 tone technique is to create a palette, an aid to the composer of 'atonal' music, not the composer of 'bad' music. Atonal music is very different from pointless music. Abstract art is very different from random scribbling. Even ugly is acceptable. It elicits an emotional response. It expresses thoughts and feelings. Pointless is not art. It's refuse. It's up to you -- the artist.