curious here, what 'atonal' works have you heard?
Schoenberg's drive toward firstly, free atonal music, and secondly, serialism can be easily understood in the context of the time. At the turn of the 20th century, chromaticism was already starting to run rampant, the works of Wagner, Scriabin, Bruckner and Mahler becoming increasingly more difficult to pinpoint in any particular key. The problem that was presented to composers of Schoenberg's generation was as such: say I want to build on the works of my teachers, but that I don't want to sound derivative all the same. What can I do now?
Schoenberg's own solution was to expand on the more unstable sounding works that had been created before him, think the stormy Bruckner 9th symphony for example, by making the music sound even more restless and even more on the brink of falling apart. The way he decided to use in order to achieve this goal was to take this drive toward more and more chromatic music to its limit: toward music that you wouldn't be able to characterize with any particular key, because it would be in a state of perpetual movement between any of them, changing key so often that you wouldn't be able to ascribe any tonal center to it.
It's easy to see that this type of composition; free atonality, is a very taxing one for the composer. Without an overall governing principle, trying to build music that lacks a tonal center is an arduous task. Schoenberg also realized that more and more often his compositions were starting to use all the notes in the chromatic scale one after the other without any particular one repeating itself before all the other ones were used already. This was a particularly efficient way to create the type of unstable sounding music that he was looking for. When on top of that, you add his own propensity toward the technique of the variation, it's easy to see how the idea behind 12-tone music came to be. Music was to be built from building blocks constructed using all the notes of the chromatic scale without repetition. One would then use this 'series'or 'tone row' and do a whole lot of stuff to it with transpositions, inversions and retrogrades. This was a great discovery when you think about it, no longer did the composer need to focus on the tonal aspect of his work, he was thus free to explore every other aspects of composition!
In my mind, the Schoenberg way was a very valid way to go at this point in time (though it wasn't the only one). It gave rise to more than a few colossal works that helped to shape the soundscape of the 20th century as a whole, think Moses und Aron, the Lyric Suite (of huge inspiration for Bartok's own SQs) or the Webern Symphony.
On the apparent lack of beauty of atonal music (which I don't really feel myself, I consider that something like this
has some of the most beautiful moments in the whole history of Western Classical music), I often get the feeling that most people's problem with it has more to do with other characteristics inherent to the music than with the lack of tonal centers. Schoenberg in particular, wasn't very prone to use repetition, he would present to you a theme just once, and he'd start working on it right away, making his music a bit hard to keep track of at times. Alban Berg wrote a very interesting article on the matter here