Jennifer,
I really like your carrot analogy. People have different kinds of learning styles, but I suspect that most genealogists like genealogy because they learn best from stories and images. Give them the facts as a straight narrative and they're lost. They have to "see" it in action in order to understand it. Illustrating with marbles, or puzzles, or carrots help everyone see it.
Over the years, I've rarely met anyone who understands any of this without going over it, again and again. That's why I think discussions like this are the only way to do it. If we're not talking about how the science operates in individual cases, most people don't get how it works.
One story about myself that helped me understand some of it -- my eye color is unusual. Most people have their eye color arranged in spokes around the iris. Sometimes the spokes are fatter and sometimes they're thinner. If you look closely, you'll see that the spokes are actually different colors. It's only when you stand back that you get the idea that there is a predominant color.
The color in my eyes isn't arranged in spokes. It's arranged in a mosaic. There is white and black and different shades of blue. The overall effect can be blue or black.
In 6th grade we had to do a genetics project. You know the kind of thing -- "I got my (blue) eyes from (my mother)", "I got my (pointed) chin from my (father)", etc.
I had a hard time with that project because of my eye color. My mom has green eyes with the mosaic. (She claims hers used to be blue.) My dad had very pale blue eyes with very small spokes of white. (He claimed his eyes used to be green.) So, I was sure it was more complicated than we were being told. I argued with the teacher (and got an F for failing to understand the assignment and for being insubordinate).
Years later, I found out that geneticists had determined that eye color is much more complicated than they used to think. Ha! I was right, and I even figured it out in 6th Grade ;)
After I was tested at 23andme, I was browsing through their profile of me and found their conclusion -- "You probably have blue eyes". To me, that's a profound statement about the uncertainty that still exists. They know 15 of the genes that affect eye color, and still they can't be sure what color someone's eyes really are.