Well you are poking a hole in your arm with a sharp needle! The other reason is to do with the formulation that the vaccine is in. Certain salts needed to stop the vaccine going off or breaking down can cause ‘discomfort’ but it’s a toss up between some extra arm pain and the vaccine not working. I know which I would choose!
The piercing of skin is always a bit hurtful, either on vaccines or drawing blood.
But the main reason that causes you to feel pain and get a bit of a swallowed arm it’s because of what vaccines actually do. The whole point of vaccines is to activate or develop an immune response – some degree of local inflammation helps recruiting immune cells to the area.