Curt's already answered it, but on this I agree with him so I'll repeat the point. *You* say that "sexual impurity" must include sex outside marriage. But we're not talking about *your* views, are we? We're talking about what the *Bible* says, aren't we? So why not show us the Biblical passage that states that sex outside marriage is wrong?
You can't assume that the Biblical writer shares your views. I don't think that sex outside marriage is wrong. Am I therefore entitled to assume that Paul must share my view, simply because I think it's right? Of course not - I should look at what he actually says. And in the event I find that he says nothing whatsoever on the subject. If you want to claim Paul as an ally in your belief on this matter you must provide evidence, not simply assume that he shares your views.
Once again, typical fundamentalist argument: (1) The Bible says X (2) I know that Y is true (3) Therefore, X must mean Y (4) Therefore the Bible agrees with my view (5) Therefore the Bible is right. As usual, no attempt to actually see what the Bible says - as usual, an attempt only to impose upon the Bible one's own views which have been formed independently.
The notion that sex outside marriage is always wrong has been around for a while among Christians - you can find it in various medieval writers - but only relatively recently (since around the eighteenth century, perhaps, and since the nineteenth century in a more mainstream trend) has it been a *majority* view among Christians. Basically, it is a social more which has become confused with Christianity. But as we can see, it is not something that comes from the Bible, and even among the church fathers, the only one I can think of who explicitly condemns sex before marriage is Clement of Alexandria. Of course, he also condemns sex in the morning and having people pour water over you in the bath, so I don't see that we should take this as normative. In fact, the early church generally condemned (or at least strongly disapproved of) sex in general, whether inside or outside marriage. See the well-known controversy between Jerome and Jovinian, for example.