I know one very effective way: Action.
I’ve found this over & over: fear can freeze you up, or you can use it to galvanise you into doing something about it.
We are often afraid of things till we do them, then they are just things we can do.

I have a long-time private client who suffers from anxiety. She started yoga to help her manage that anxiety, and with the help of her regular practice, was able to come off her medication. Pretty cool huh?
I’m not saying this would be the case for everyone: some people, me included, have very weird brain chemistry, and might never be ‘normal’. Who cares really, as long as you can find a way to be in the world in a more comfortable and secure way.
This student’s main goal was to learn headstand.
Why?
It terrified her.
She wanted to overcome that.
Once we had established that there was no physical reason she couldn’t do it, we went about building the strength she needed for the pose.
And yes, she can do it now. It doesn’t scare her anymore.
She’s not even particularly impressed that she can do it!
She’s set her sights on handstand now.
Because that scares her too.
Not for long, I suspect.
Action cures fear, as long as you are taking safe actions, of course!

Moving from Stability: Understanding the Pelvis in Posture (Online workshop)
Light Up Your Life

That was exactly our theme in one of my most recent yoga classes. Letting go of our anxieties and go do “it” (whatever scares you). It was to pave the way for some major arm balances, which worked out pretty well once we let them happen and stopped worrying about falling.
Your yoga teacher was a little bit sneaky! I totally approve…