Music, for the longest time, much like visual art, was determined on its quality by whether or not all of the imposed rules were followed. However, Arnold Schoenberg came along and completely ignored those rules, despite following them in the past. Even though there have been many artists before Schoenberg that have included dissonance (for example, between the strings and woodwinds in the development of Mozart’s Symphony No. 40 in G minor), Schoenberg created the ultimate amount of dissonance by creating notes that never seem to resolve. In fact, they almost seem as if the notes were simply strewn everywhere. He intentionally creates this constant dissonance in order to create a reaction from his audience. I would not necessarily go to say that he is an expressionist, as none of his work appears to portray his mood or inner voices.
As for Pierrot Lunaire, the text and the music do not truly connect. When reading the poems, a giggle is elicited, a feeling of amusement bubbling up. On the surface the text is about a silly clown, and that is all it may be. However, Schoenberg takes it a step further and composes pieces to accompany the text that make it sound like Pierrot is not all quite mentally there. It makes the audience feel a great amount of discomfort, not only with the music itself, but the disparity between the music and text.
A possible reason that people might have been behind Schoenberg is because, unlike other art forms, there does not have to be a meaning behind the composition. It is the purest form of art. Therefore, even if the music is very unpleasing to the ear, it is still music, and does not need an excuse for why it was written like that.