In this context one should note that the first person narrator starts with a confession: He admits that he is an inmate of an asylum. (Could anyone please quote the translated sentence? I've only got the book in German. Thanks.)
Oscar's first statement makes him a highly unreliable narrator. With this first sentence the author asks the reader to question everything Oskar says. So I think you are quite right to ask that question, Scheh, and I would have given a similar answer. Oskar wants to make us believe that refusing to grow was an act of protest, against his family, especially his father, and against the regime and that he needs his drum to express himself/his protest, eg when he disturbs the Nazi meeting by confusing the march music with his waltz rhythm. But is there really anything behind this so-called protest?

