Your question is a little bit backwards. It's not that there is a ruling to grant people a "right" to "practice law" on their own behalf; rather, there is an absence of a ruling denying them the right to speak for themselves in court. Courts and similar legal hearings existed before there was a legal profession; in the beginning, one pleaded one's own case because that was the only way. As laws became more complex, specialists arose who by virtue of their expertise acquired the right to act on behalf of a party to an action, that is to say, to act as that person's attorney at law.
While some jurisdictions may have decided to remove litigants' ability to have access to the court without the aid of a specialist (that is, of a qualified lawyer), the United States has not chosen to do so.
I will echo the other answer in saying that the "practice" of a profession generally means the provision of services to others for some consideration. Representing oneself in court is no more the practice of law than is bandaging one's own wounds the practice of medicine.