The debate between Cessationism (the argument that the extraordinary gifts of the Spirit have ceased: prophecy, tongues, miraculous healings) and Continuationism (the argument that all the gifts of the Spirit continue today) is a minor debate among Christians. It should not be a source of division, but more of a friendly in-house debate among brothers. So with that in mind, here are two positive arguments and one negative argument for Cessationism:
(1) In Ephesians 2:20, Paul describes the church as "built on the foundation of the apostles." The structural metaphor of a foundation means that the ministry of the apostles was a once-and-for-all period in redemptive-history. To this apostolic ministry, there are "signs and wonders" associated (Acts 1:8, 2 Cor. 12:12). Therefore, by logical necessity, these signs and wonders have ceased with the ending of the Apostolic Age. These signs and wonders are prophecy, tongues and miraculous healings.
(2) Revelation is God's Word. Revelation in the New Testament era is restricted to the Apostolic Age. Thus, the New Testament is a closed book because the Apostolic Age has ceased. Prophecy is also revelation (Eph. 2:20, 3:5). So too tongues (1 Cor. 14:21-22). All revelatory gifts have ceased.
(3) Continuationism proposes that all the gifts of the Spirit continue today, including all the signs and wonders described in Acts. But inevitably, certain concessions must be made. The NT writings have ceased; the apostles have ceased; infallible prophets have ceased; tongues as the gift of foreign languages have ceased; people rising from the dead have ceased; the intensity and amazingness of signs and wonders have ceased. Therefore, Continuationists must concede a kind of partial-Cessationism. In other words, there are no truly principled Continuationists – only varying degrees of Cessationists. Which means the Cessationist argument is essentially correct.