Deductive Bible study is another name for topical study of the Bible. It starts by taking a topic and then digging in deeper to what the Bible has to say about that topic. Deductive reasoning starts at a more general level and then goes to specifics, for example taking a universal statement and then finding evidence to support (or disprove) it. Deductive Bible study uses this approach in studying the Bible.
Conversely, inductive Bible study looks at a specific passage to understand it. From there, more general truths can be extrapolated. Both types of Bible study are useful in our study of the Scriptures.
When doing a deductive or topical Bible study, it's important to start with a topic that is biblical, and it's important to not have a preconceived idea of what the answer or result of your study will be. One weakness of deductive Bible study is that it can allow for people to essentially make the Bible say what they want it to say—rather than arriving at the truth. In short, it can lead to the error of eisegesis. This is something to be aware of in personal study and in teachings from the pulpit. Paul warned Timothy: "For the time is coming when people will not endure sound teaching, but having itching ears they will accumulate for themselves teachers to suit their own passions, and will turn away from listening to the truth and wander off into myths" (2 Timothy 4:3–4). In order to be truly successful with a deductive Bible study approach, you should start with a universal truth within the Bible and dig into the details from there.
A deductive Bible study may begin with an idea or phrase and then the student looks up passages in the Bible that address said phrase to better ascertain what it means and how it applies to our lives. For example, you could start with the phrase "God is love" (1 John 4:8), and then study all of the passages within the Bible that talk about the love of God and show what His love looks like in practice (i.e., Jeremiah 31:3; John 3:16; Romans 5:8; 1 John 4:19).
As you can see, deductive Bible study is especially useful when it comes to studying large topics within the Bible. It can help you get a better overall perspective of the topic as well as help you narrow your focus to better understand the specific facets that fall within that topic.
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