Counter-intuitive: ask most people what is the first thing they do
when making a turn on a bicycle (or motorcycle) and they'll either say
"turn the handlebars in the direction I want to go" or "lean in the direction
I want to go" - both are wrong. That's not really what you are doing!
What we are forced to learn as youngsters but rarely realize consciously is that the FIRST action when you want to turn on a two-wheeler is to turn the handlebars in the OPPOSITE direction. This puts you out of balance, causing you to lean in the direction you actually want to go and, by compensating with the handlebars, you initiate your turn. (Look up "counter-steering".)
I didn't learn this until I took a motorcycle safety course with Maria after a lifetime of cross-country riding. I had no idea.
The immediate benefit was that I became 1000% better at dodging potholes: For a quick change in direction, push down on the handlebar on the same side as the direction you want to go - to dodge right, push down on the right hand handlebar.
(Second benefit: great cocktail party riddle.)
Are you teaching a youngster how to ride a bicycle? IMHO: Teach them counter-steering from the get-go (and ditch the training wheels, they will interfere with understanding how it all works).
P.S. Some folks say, it is POSSIBLE to turn a 2-wheeled vehicle with "handlebar steering" (turning the handlebars in the direction you want to go), but, IF that's true, it's true only if you are creeping along at a very slow speed. Part of our learning to ride involves learning to counter-steer (frequently unconsciously).
Here are the physics: https://www.youtube.com/watch?v=ZpV2Bg-WX0w