I want to explore this in a couple of directions, theological and Biblical.
1. The most basic activity of the church is listening or hearing. The church, and the individual Christian as a member of the church, hears God's Word and is gripped by it, energised by it, given new life by it - not just once, but again and again and again. The church always continues to be hearing. But because the church hears, the church must also speak. It is the nature of the Word that the church hears that it becomes at once the Word that the church must speak and witness to and announce to the world. This is true both because the content of that Word includes a specific commission to speak, and because the Word comes with transformative power that naturally leads to speaking. Hearing necessitates speaking. But if hearing necessitates speaking, it also controls speaking: only what is heard is spoken. When speaking goes beyond hearing, we are outside the range of Christian activity.
2. The book of the prophet Jeremiah most clearly illustrates the point, in the contrast between the false prophets and the true prophet. The Lord's main complaint against the false prophets is not that they are lying - although that comes up! - but that they are speaking without commission: "I did not send them, nor did I command them or speak to them" (14:14). "For who among them has stood in the council of the Lord, to see and to hear his word..? I did not send the prophets, yet they ran; I did not speak to them, yet they prophesied" (23:18-22). By contrast, Jeremiah cannot help but speak (20:9). He has heard God's Word, and he must proclaim it. He is compelled to do so. His commission as a prophet obliges him to speak.
3. The NT is clear that this is what it means to be apostolic: "we cannot but speak of what we have seen and heard" (Acts 4:20); "For if I preach the gospel, that gives me no ground for boasting. For necessity is laid upon me. Woe to me if I do not preach the gospel!" (1 Cor 9:16).
This shuts the door to speculation in theology - if we are not forced by the Word of God (which concretely means by the content of Holy Scripture) to speak on a subject, we would do better to remain silent. It also shuts the door to a 'quiet faith' - if we are truly hearing God's Word, we must speak.