One of the ways that I address the whole Copyright vs. Fair use when teaching the concepts is to have students think about whether or not the use will have a negative impact on the original author or copyright holder. I ask the question: Is the way I'm using this work going to cause the creator/copyright holder to lose out on being credited for the work, lose out on making money because of my use, or am I going to make money on that use that won't be fair to the creator? If I can answer yes to any of these questions, then it probably isn't fair use.
So, for teachers, you have to think about who the copyright is protecting and why it is protecting them. Textbooks, for example, are protected so that the company doesn't sell one book to a school and then the school makes copies. The company wants us to pay for each use and when we photocopy their book, we are causing them to lose out on profits. The same would go for music publishers (sheet music for example), they make money on bands paying for each sheet so when we copy, even if for educational purposes, they lose money.
When we make small copies of original works to prove a point, however, we are not taking away from anyone's profits, and if we are doing it correctly, we are even attributing those creators for their work. In many ways, when we adhere to fair use, we are actually creating more business for the original creators. I can think of many times when I heard or saw a small clip of something, liked it, and then went out and rented the movie or bought an album.