to talk something through with others: to reason, discuss, and argue a case back and forth
At its core the word means to talk a matter through: to lay out a case and follow the give-and-take of reasoning with other people. In Acts it is Paul's signature method. Sabbath after Sabbath he "reasoned" in the synagogue, opening the Scriptures and pressing the argument until his hearers were either persuaded or provoked. This is not a lecture and not a modern open-ended chat; it is persuasion by argument, aimed at conviction. Unlike simply announcing a message (κηρύσσω), this verb pictures a speaker engaging objections and working an argument through with the people in front of him.
The same verb can name a heated quarrel. On the road the disciples "argued" over which of them was greatest, and in Jude the archangel Michael "disputed" with the devil about the body of Moses. Whether the exchange is friendly teaching or open conflict, the constant is reasoned back-and-forth, one side answering the other. That is why English translators reach now for "reason," now for "discuss," now for "dispute," depending on how warm or cold the room is.
Once, in Hebrews, Scripture itself is the speaker: the written word "addresses" the reader the way a father reasons with his sons. Here the exchange runs one direction, from the page to the heart, but the picture of a personal, reasoned appeal remains.