When will using logic help you persuade someone? If you’re talking with someone who says, “I’m going to need to see data to support that,” it may be the case that they do, in fact, have a reservation that can be resolved with more data. The additional information may allow them to set their mind at ease.
On the other hand, they may just be saying they want to see more data because they don’t want to do what you want them to do. If this is the case, giving them more data isn’t going to help your case, because they will come back with, “well, that data doesn’t prove anything” or something similar.
Logic, data, reason…to be convinced by these, a person has to be open to being convinced by them. And the necessary openness might not be “switched on” by logic, data, or reason.