Can a court order me to submit a handwriting sample? Why wouldn't that be classified as self-incrimination?

Yes, you can be ordered to provide a sample of your handwriting for identification purposes. Such an order does not violate the Fifth Amendment protection against self-incrimination. The privilege against self-incrimination applies only to testimonial evidence and "compulsory communications." It does not apply to physical characteristics that might identify you, such as your fingerprints, voice, handwriting or dna. Both federal and state courts have usually held that the Fifth Amendment offers no protection against compulsion to submit to fingerprinting, photographing, measurements, to write or speak for identification, to appear in court, to stand, to assume a stance, to walk, or to make a particular gesture. The distinction, expressed in various ways, is that the privilege is a bar against compelling "communications" or "testimony," but not to compelling "real or physical evidence" from the suspect. Put another way, the privilege against self-incrimination is directed at the use of legal process to extract an admission of guilt from the person's own lips or other communicative act. A mere handwriting or voice exemplar, in contrast with the content of what is written or spoken, is an identifying physical characteristic outside its protection.