This point makes literally no sense to me. He says don't start coding before you fully understand the problem, and then he says the way to explore the problem space is coding (the code-test-improve cycle).

By the way I agree with the last part. Sometimes the best way to understand the problem is writing a half-broken solution for it. You just have to be aware that what you're writing probably won't solve the problem, and make sure all the other stakeholders are aware too (that's usually the hardest part).