Some fears of mine: STDs, car crashes, losing my job, getting in trouble, harsh conflict, social ostracization, my kids getting hurt, getting sick, dying, losing my laptop, I mean I could go on and on. I think most fears are so rational and obvious we forget to even classify them as fears, instead reserving that label exclusively for irrational fears.
Out of the emotions, the feeling urging us to avoid negative consequences seems pretty useful haha
The example was public speaking. Many people get very anxious if they need to do that. But if they think about it rationally they realize there is no real danger there. That's how they know it is an irrational fear, and they can use the breathing technique to make it managable.
So maybe it's more about if you know you should not or can not run away from a fearful sitution you should take a deep breath. Whereas if you are on a dark street alone and a group of hooligans look like they might attack you then feel fear and instead of breathing deep, you should run.
I'm not sure if that's true. I don't really get stressed or anxious, and from the few times I tried to put myself into stress mode I've performed much worse.