The 3-hour rule does NOT mean you have to eat every 3 hours, whether you're hungry or not.
The 3-hour rule does NOT mean you can't eat anything until 3 hours after a meal.
So what DOES the 3-hour rule mean?
Since I'm a visual learner, I thought I would show you a picture of how I like to think about it (See Example 1 below.). Let's say I eat breakfast at 6:00 am, lunch at noon, and dinner at 6:00 pm. The "bubbles" in the diagram below represent each meal and the 3-hour window around each meal. So, basically, if I eat a snack during one of these "bubbles," I have to have the same fuel as the meal in that bubble or have a FP snack (FP snacks can be eaten anytime. They are immune to the "bubbles."). So if I wanted a snack at 10:00 am, for example, it doesn't matter what fuel I had for breakfast, because it's been more than 3 hours since breakfast. It DOES matter what fuel I plan to eat for lunch, though. If I plan to eat an S lunch, I should eat an S snack. Make sense?
So also in this example, if I wanted to eat a snack at 2:00pm, I would need to have the same fuel that I had for lunch. But if I had my snack at 4:00 pm, I would need to have the same fuel I plan to eat at dinner.
Please note that I don't HAVE to eat a snack at all. Nothing in THM requires me to eat every 3 hours or at any specific times.
Now let's make it a little more difficult. What if I eat my breakfast at 7:00 am, lunch at noon, and dinner at 5:00 pm? Then the bubbles will look like Example 2 below and overlap. So if I wanted to eat a snack at 9:30 am, I would have to be careful about the fuel I had for breakfast AND what I plan to eat at lunch. If I had an E breakfast but I plan to eat an S lunch, a snack at 9:30 would need to be a FP so that it wouldn't interfere with either "bubble." But if I had an S breakfast and plan to eat an S lunch, I could have an S snack at 9:30 if I wanted one.
I hope this clears up confusion and doesn't make it more confusing. Like I said, I'm a visual learner/thinker. If this confuses you, just pretend you never read it... :)