Some people (like you and me) are lucky because we haven't really needed the doctor. I've only gone a few times in my life, for things like my sleep disorder, an on-going problem with my left ear, and a time I fell while running for the bus and the wounds on my knees got infected. For all of these things, I wouldn't have been able to go if I hadn't been provided with health insurance. I surely pay more through taxes for my insurance than I use, but I'm okay with that.
By the way, you say you're upset that you pay for something you don't use; so if it wasn't public in Canada, you just wouldn't have health insurance at all? If you got private insurance, you'd still be paying for something you don't use... and if you were in the US, you couldn't just wait until you got a disease, due to the "pre-existing condition" clauses. It's dangerous to go without health insurance.