Subject as a term applying to Republican Freemen was not used because of its association with British royalty. Republican Freemen are “NOT” subjects.
From the birthers favorite case, Minor:
“For convenience it has been found necessary to give a name to this membership. The object is to designate by a title the person and the relation he bears to the nation. For this purpose the words “subject,” “inhabitant,” and “citizen” have been used, and the choice between them is sometimes made to depend upon the form of the government. Citizen is now more commonly employed, however, and as it has been considered better suited to the description of one living under a republican government, it was adopted by nearly all of the States upon their separation from Great Britain, and was afterwards adopted in the Articles of Confederation and in the Constitution of the United States. When used in this sense it is understood as conveying the idea of membership of a nation, and nothing more.”
But as I have shown already, the term ‘natural born subject’ was, for some years after, used interchangeably with NBC.