It is still irrational, to be frightened of something which cannot or will not hurt you. I don't like cats, I am not afraid of them in the slightest, but for me it's a dog every time. As a child I was was quite scared of lifts, only because I had never been in one until I started work. Once working, I got used to them, I even got stuck in one a couple of times, no problem, not a concern. I studied how the work, the safety features, realised that even if the rope snapped, they couldn't fall, so apart if there is a fire - probably the safest place to be in any building.
An irrational fear is to be frightened of something, which cannot/will not hurt you. Some dogs will hurt you, but almost without fail that is because they have been bred or trained to do that. A BC is bred to keep sheep herded together and will gently nip the ankles of any which try to stray from the flock. My BC will nip my nose gently sometimes, when I tease her. If she needs anything she never whines, she taps me on the arm or leg. She never barks, apart from when something concerns her. If one of her toys or balls, get under some item of furniture, she stands and stares at me, to get my attention, then points with her nose or a paw at where the toy is.
If you go out as a group with her, she will encourage the stragglers of the group to keep up. Her bigger, much older brother was an escape artist, nothing you could do would keep him in the garden if he wanted out. He often took himself out in the late evening, spend the entire night roaming, then come back next morning, sometimes having paid a visit to relatives at the far end of the village. He knew the roads and paths better than me.
She is the same, except she would never attempt to go out by herself, but a complete stranger can put her on a lead and she will take them out for a walking tour of the village without getting lost.