I think OP might mean the natural aliasing that happens when you rotate without linear filtering.
This happens because of rendering logic in your game engine, not because of any specific tool you're using to make the animations. (to be sure absolutely sure of what it looks like, you may even have to see it in-game 'cause camera stuff and varying resolutions might affect it)
It's happening to all rotating parts. It's just that the shoulder is rotating between angles where rows and diagonals of pixels will inevitably be represented that way and move that way.
I don't have a lot of experience actually doing pixel art but I'm thinking there are things you can do to reduce the effect. (maybe something about the texture sizes or making some special rendering code.)
IMO, I think it looks fine. It's part of the aesthetic. If it happens too often or looks too weird to you, you can make sure the images minimize slow movements in certain angles. That's something you can easily do and preview with Spine.
Spine would be a really great option if you're animating stuff like that.
