You can't be more committed to fixing a prospect's problem than they are themselves. If you are, you'll end up in a bad situation at some point.
A client of mine creates websites, among other things. He recently spoke with a prospect who called him about a new website.
My client kept asking him questions, and uncovered two things. First, the prospect really needed a new website. His website was over ten years old, and wasn't doing anything for him.
However, my client also got the sense that the prospect didn't really think he needed a new website.
Finally, my client asked him, "It doesn't sound like you're hurting for business. Why do you think you need a new website?"
His prospect responded, "Everyone else keeps telling me I do."
"What do you think?" my client asked.
"I don't really care," the prospect responded.
My client knew he could help the prospect. But my client cared about it more than the prospect did!
When I run into a situation like that, I am careful with my tonality, but I call the prospect out.
I say something like, "I could be way off here, but I get the sense that fixing this problem is more important to me than it is to you. Can you help me understand that?"
When I do that, one of two things happen. Either we refocus the conversation pretty quickly, or we're able to figure out that we shouldn't be talking.
If the problem they bring you isn't actually a big deal to them, figure it out quickly, so you don't waste your time or theirs.