The person who keeps pressing after an answer has changed the nature of the request.

A request is an offer that can be refused, and that is what makes it a request. Once an answer has been given and the asking carries on, the thing has quietly become something else: a test of your stamina rather than a question about your preference. Persistence gets defended as enthusiasm, though its actual effect is to make each refusal cost more than the last. The change of category is worth noticing.

You can repeat your answer without supplying new reasons, and you can stop replying altogether. If the pressing continues, say plainly that the answer is not going to change.