I wanted to start by establishing what you meant by tongues. Usually people mean either 1) angelic prayer language that occurs in the middle of the church service by a pastor preaching or by those in the congregation who are “in the Spirit” and the result is a prayer language that is unintelligible to any observer. 2) a foreign language that is known to other men on earth (i.e. Spanish, Russian, English, Urdu, Marathi, Tagalog, Sena, etc).

Onto the confession you asked about, the WCF (Westminster Confession of Faith) states the following:

1.1 Although the light of nature, and the works of creation and providence do so far manifest the goodness, wisdom, and power of God, as to leave men inexcusable; yet are they not sufficient to give that knowledge of God, and of His will, which is necessary unto salvation: therefore it pleased the Lord, at sundry times, and in divers manners, to reveal Himself, and to declare that His will unto His Church; and afterwards, for the better preserving and propagating of the truth, and for the more sure establishment and comfort of the Church against the corruption of the flesh, and the malice of Satan and of the world, to commit the same wholly unto writing; which maketh the Holy Scripture to be most necessary; those former ways of God’s revealing His will unto His people being now ceased.

The question still remains, “why does the confession state this?”, or “how did those writers of the WCF come to this conclusion?” Allow me to provide the biblical support given for this conclusion and maybe we can go from there:

John 20:31 but these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.

1 Cor 14:37 If anyone thinks that he is a prophet, or spiritual, he should acknowledge that the things I am writing to you are a command of the Lord.

1 John 5:13 I write these things to you who believe in the name of the Son of God that you may know that you have eternal life.

1 Cor 10:11 Now these things happened to them as an example, but they were written down for our instruction, on whom the end of the ages has come.

Heb 1:1 Long ago, at many times and in many ways, God spoke to our fathers by the prophets, Heb 1:2 but in these last days he has spoken to us by his Son, whom he appointed the heir of all things, through whom also he created the world.

Heb 2:2 For since the message declared by angels proved to be reliable, and every transgression or disobedience received a just retribution, Heb 2:3 how shall we escape if we neglect such a great salvation? It was declared at first by the Lord, and it was attested to us by those who heard, Heb 2:4 while God also bore witness by signs and wonders and various miracles and by gifts of the Holy Spirit distributed according to his will.