Um, really ignorant question here, but what book on reasoning can I read to be able to see through arguments and debates like you just did? I want to learn about empirical and normative questions, etc.
I'll give the same advice I give as a teaching grad student to undergrads who think us grad students are incredibly smart: it only takes a tiny amount of knowledge or training for someone to have that you don't for them to seem so much smarter. Don't be fooled. As a grad student enslaved by a university, I have become quite familiar with all the arguments about the purpose and place of research vs. teaching.
Anyways, this confusion between normative and empirical claims is extremely common; once you become aware of the difference, you see it everywhere. The easiest way to familiarize yourself with this and related ideas is to take a introductory course on moral philosophy or read an introductory textbook. Unfortunately, even if I thought the book I used in college was all that great (it was OK), I forgot the name of it. The material is fairly universal at the introductory level, though, so any decent book would do.
As a student about to start on the honours portion of my degree, I find solace in analytic philosophy (as opposed to those damn ethical/post-modern philosophers).