I've been quite a few posts like this one on Reddit. People are often confused by the fact that you can't equip a chestplate core, and I think the main reason is the appearance. It looks like a recolored chestplate.

All of the other Tinkers' tool parts are obviously not complete tool at a glance. Pickaxe heads aren't confused for pickaxes because they lack a handle, for instance. Armor cores need a similar visual indicator.

I recommend renaming them to "armor frames" and cutting a hole out of the center of each texture. Thematically this would make sense, since you patch those holes with armor plates when you make the armor.

I've been thinking the same thing for a while also. Personally I'm not sure why people are confused since making armor is just like making any other Tinkers' tool, but I can recognize that the appearance of the armor cores can be misleading. I don't think I want to change the name, at least for 1.12.2, but I'll look into updating the textures at least.

I get the impression that most people who get confused aren't very familiar with Construct's Armory. They just see a chestplate shaped thing. This is the only mod I'm aware of where chestplate shaped items can't be equipped as armor.

I guess it's part of the language of modded Minecraft. Mods have reinforced the idea that armor comes in a specific shape, and people assume items with that shape work as armor.