To understand countersteering and getting used to it so that it's 2nd-nature, practic in big parking lots. Get up to 5mph+ and ride with your hands lightly on the handlebar. Let go of one hand (let's say left) while keeping the other one near, stay in a straight line. Now, with right hand, push on the bar so that it turns the bar left. Which way does the bike lean and which way does it turn?

Now do the opposite, pull on the bars so that it turns the bar right (not as easy to do). Which way do you lean and which way does the bike turn? Repeat with only the left hand on the bar, push on it, pull on it and see which way the bike leans and turns.

What happens on the bike a lot of times is that both hands ends up pushing and they fight each other and you end up going straight instead of turning. Or you try to consciously turn the handlebars in the direction you want to go and the bike refuses to respond that way.

It's pretty simple physics if you imagine looking down on the rider from above. The front & rear contacts patches are inline with the centre-of-gravity in between. Which way does the front-contact patch move when you steer left? Steer right? That explains why the bike leans to the other side and you turn to that side.