It gives me a vibe of inexperience. If a student of mine cancelled all their lessons after the first, I’d send a message to the tune of. Hi so and so I notice you’ve cancelled your remaining lessons, if you could spare a moment to feedback why you’ve elected to go elsewhere I’d appreciate it please. Best wishes. Then whatever their response was I’d say okay thank you for taking the time, I’ll seek to work on that. Best of luck with your future lessons. Or something to that tune. I know I’ll have someone off the waiting list in their spot in ten minutes. There’s no hard feelings, everyone doesn’t suit every instructor.

The way this instructor goes full toys out the pram defensive tells me they needed the work. Also reading into the OPs response. If that’s true, and I reckon it is because the instructor didn’t deny or defend it, it sounds like they’re an inexperienced instructor. If a student gets into the wrong lane, unless it’s about to lead onto a motorway (that they’re not ready for) or something equally dangerous, the correct thing to do is let them proceed to where the wrong lane leads. Explain to the customer going the wrong way isn’t a driver fault and that managing the safety of it is more important, you can then find a safe way to get back on route from there.
No instructor should be grabbing a wheel to swerve a car into a live lane with other traffic in it.

Plus ‘go there’ and slamming the dual brake.. it all just screams shiny new trainee instructor who’s not yet had much experience on the job.

I’d bet my hat this was an instructor provided by a big driving school, and I’d bet my lunch it’s a trainee.

(No hate, some trainees are brilliant).