Counter steering seems anti-intuitive to the non-rider, but they do it without thinking about it when riding a bicycle. The non-rider or new rider who thinks that the handlebars turn in the direction of the bike's turning can't understand why they should press the handlebar grip in the opposite direction. When I was an MSF instructor I used to challenge the students who already were riders, but who balked at the idea of counter steering to try to turn the handlebars of their bike when riding in a straight line at 40 or more mph. They quickly realize that they cannot actually turn the handlebars but when trying end up counter steering.
Leaning the bike in a turn seems scary to new riders. Part of the problem is that their perception of the lean angle is grossly exaggerated over the real angle. They lean over 5% and think that they were leaned over almost to the point of touching a knee down. It just takes some time and experience to get used to the leaning without worrying that the bike will be sliding out from underneath you. And riders who try to take a curve solely by leaning the bike, but without counter steering will end up not making the curve or having to slow down to ridiculously slow speeds. Learning to counter steer correctly early in the process is a valuable skill for any rider.
Leaning the bike in a turn seems scary to new riders. Part of the problem is that their perception of the lean angle is grossly exaggerated over the real angle. They lean over 5% and think that they were leaned over almost to the point of touching a knee down. It just takes some time and experience to get used to the leaning without worrying that the bike will be sliding out from underneath you. And riders who try to take a curve solely by leaning the bike, but without counter steering will end up not making the curve or having to slow down to ridiculously slow speeds. Learning to counter steer correctly early in the process is a valuable skill for any rider.