The only time you steer left to go left is if you're going so slowly that the only reason the bike doesn't fall over is because of your near-superhuman balance. That is to say, when you're practically at a standstill. Anywhere approaching walking pace or above, if you try to turn left by steering left, you'll fall off the right hand side before you make any appreciable turn.
That's the issue; how do you lean left to start with? If the human-bicycle system has its center of gravity over the wheel line, shifting your weight relative to the bike doesn't move the center of gravity - you lean one way, the bike leans the other, and you end up in the same overall position. The only way to initiate a lean to the left is to countersteer to the right.
You are. I proved this to myself once by applying pressure to the handlebars using only the palm of my hands on the backside of each handle. Even at very slow speeds, I could not for the life of me turn left by applying pressure only to the right bar (to turn the front wheel to the left). No amount of leaning helped. To lean the bike, I needed to create some external force to push it over. Leaning my own body to the left just made the bike lean to the right.
Some people seem to describe this difference as unconscious countersteering versus deliberate countersteering, that is, that the difference isn't really whether you're countersteering or not, but whether the countersteer is large enough that you have to do it "on purpose".
The only time you steer left to go left is if you're going so slowly that the only reason the bike doesn't fall over is because of your near-superhuman balance. That is to say, when you're practically at a standstill. Anywhere approaching walking pace or above, if you try to turn left by steering left, you'll fall off the right hand side before you make any appreciable turn.