I know what you mean. I have injected insulin on myself for over ten years and don't bat an eyelid.
I get the flu jab once a year and I'm all nervous and look away.
I assume it is about being in control and knowing exactly when the needle is going in.
However easy it is, I would rather not bother.
Although happy to stab myself, I really hate blood tests, I had to have some tests done one morning when it was really cold and the nurse couldn't find a vein in a number of places, so ended up running up and down 4 flights of stairs to get the blood pumping, it worked..