The Reformed Presbyterian Church (in America) was relatively small in the 1800s. (It was less than 1/3 of the size that it is today). There were only four established seminaries in the United States at the time RPTS's Constitution was written (in 1807). The country was young and the Church was getting accustomed to life in the United States- there was a lot going on!
So why would a small Presbyterian denomination see a need for training her pastors in a way other than one-on-one in a pastor-student mentorship? Why take on the financial, ecclesiastical, and time related responsibilities? Besides the obvious reasons of allowing those who excel in languages, biblical studies, systematics, and ethics each train in their area of expertise- there was also another reason. The RPCNA view of the end-times would come into play. Their eschatology required more men for the ministry:
"There was a belief that, because of the power of truth and reason, the denomination could have a genuine impact on society. Most important, perhaps, was the prevailing eschatology of Covenanters, which was Postmillennial- that is they believed that the 'thousand years' of peace and righteousness which precede the return of Jesus Christ was to be ushered in by the efforts of Christians. They also believed that the millennium was near... In this context, it is easy to understand why the church felt not only that a theological seminary could be supported, but also that it was bound to grow and have an influence far beyond the tiny denomination which gave it birth." (R.M. Copeland, Spare No Extertions)