If I hit my head, it would hurt.

Suppose I had a bat. I selected this bat at random from a pile of bats between 12 inches and 12 feet long, but on average it's probably about 3 feet. I suppose that the bat is made of an alloy which is at least 3 percent titanium. I will approximate the shape of the bat by a cylinder. If I hit my head with the bat, it would hurt.

Why do I have such trouble convincing people that a more general statement is sometimes easier to understand than a specific case?