Paul, who is also a Jew, has studied the Hebrew Bible his entire life, but when he met Jesus his view on the Bible drastically changed. The message of the biblical story came together for him as he realized that the death and resurrection of Jesus were the key missing pieces. Therefore, when Paul is preaching and teaching to the Berean Jews, he wants them to have the same realizations that he did. He does not cast the Bible aside as irrelevant or outdated, rather he presents the message of the Bible in its fullness, a message that is fulfilled in the death and resurrection of Jesus Christ.
Many Christians these days rush to sources other than the Bible - every believer must hear what is in the Scriptures, and to examine carefully then to live accordingly. It was with this good intention that the Church of Antioch was founded.