The presbyterian argument rests on a philological observation that is not really disputed. In the letter to Titus, Paul instructs that elders be appointed in every town and then, in the next sentence, gives the qualifications of an overseer, using the two words of the same people. In Acts the elders of Ephesus are summoned and then told that the Spirit has made them overseers of the flock. The letter to the Philippians greets overseers and deacons with no third order between them. On the face of the texts, episkopos and presbyteros name one office.
A threefold order appears clearly in the letters of Ignatius of Antioch, from the early second century, where one bishop stands above a council of presbyters and a body of deacons and nothing is to be done without him. Episcopal churches read that as the apostolic arrangement coming into focus; Reformed churches read it as a development, and hold that ordination by a plurality of presbyters is therefore sufficient and that a bishop is a presbyter with a wider charge rather than a distinct order.
The congregational position moves the question again. If the church is the gathered congregation, then recognising a person gifts and calling belongs to that congregation, and ordination is confirmation rather than the conferral of a character. Modern agreements between churches have generally proceeded by mutual recognition of ministries rather than by settling the argument, with the Porvoo agreement and Called to Common Mission each finding a way for churches with and without the historic episcopate to accept one another ministers.