While none of the reasons listed below are sufficient in themselves to justify interactive preaching, together they form a strong challenge to cultivate verbal interaction with the congregation on a regular basis. I hope you feel the weight of the argument.
Jesus' preaching. In his teaching/preaching ministry, Jesus continually interacted with his audience. For example, in speaking to the Jews who believed him (John 8:31-41), Jesus allowed both questions and comments from his audience. Sometimes those who interacted with him were hostile to his message, but he provided them plenty of opportunity to question and comment. Whether Jesus was preaching as we understand preaching is questionable. But even in the synagogue, where he was definitely preaching (Luke 4:16-27), there appears to have been some sort of verbal interaction.
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Paul's preaching. Debate appears to have been an important component of Paul's evangelistic preaching. In Acts 18:28, Luke says that Paul vigorously refuted the Jews in public debate. Again, this may not have been preaching, but it is difficult to believe that the skeptical and hostile audiences to whom Paul preached, listened silently to his preaching without any verbal response. Paul seems to have been at his evangelistic best in dialogue, "proving from the Scriptures that Jesus was the Christ" (Acts 18:28).
Priesthood of believers. One corollary of the doctrine of the priesthood of believers is that because every believer has the Holy Spirit, God's voice is best heard corporately through believers together under the authority of His Word. While this has ramifications for decision-making, it also may affect the way we hear God in preaching. Does the body (congregation) have a role in explaining, illustrating, and applying God's word in preaching? If so, how can it be done better than through interaction in preaching?
The form of the passage. Some biblical texts contain dialogue. For example, much of the teaching of Jesus arises within the context of dialogue with his audience. It may be possible to reflect this dialogue in sermonic form so that the form of the sermon reflects in some way the form of the passage. There are also many teaching passages in which illustration and explanation is given from the experience of the audience (e.g. James 5:7-11). It would be appropriate to mirror this technique by asking the audience to supply the illustration and explanation.