There are at least two major advantages of asking open-ended questions when you are interviewing a suspect or a potential witness.
First, when you ask such questions, you do not lead the person that you are interviewing as much as you would if you asked more closed-ended questions. What this means is that you are much more likely to find evidence to support theories that you have not already devised. If you ask only closed-ended questions, you might miss evidence that is not easily elicited by the questions you have already thought to ask.
Second, when you ask such questions, you are more likely to get a suspect to slip. If you ask really simple questions that can be answered with a “yes” or a “no” you do not encourage the suspect to really talk. If you ask broader questions, you are more likely to get them to open up. When they open up, they might talk too much. They might let out details that they would not otherwise have mentioned. They might say things that contradict other statements that they have made. In other words, you are giving them more opportunities to say things that will help you and hurt them.