JDON, I think it is because majority of peeps are right handed, so if there is any reaction, i.e. soreness or bruising, then it is less likely to feel worse using that arm so much.
I usually ask for it in my right, being left-handed.
My hubby had to have a course of jabs over a week (every other day), and just so he didn't get bruising building up they alternated from right to left.
When in hospital, having morphine jabs in my backside every few hours they also alternated which cheek!!! LOL